Recent questions tagged vector-product

A tow truck drags a stationary car along the road. The chain makes an angle of 30 degrees with the road and the tension in the chain is 1500 N. How much work is done (in Joules) by the truck in pulling the car 1 km (approximate answer, rounded off)?

asked Feb 11, 2014 by balaji.thirumalai

1 answer

The volume of a parallelopiped formed by $\hat i+a\hat j+\hat k,\:\hat j+a\hat k\:and\:\:a\hat i+\hat k$ is minimum if $a=?$

asked Jan 13, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow u=\hat i+\hat j,\:\overrightarrow v=\hat i-\hat j\:and\:\overrightarrow w=\hat i+2\hat j+3\hat k$ and $\overrightarrow n$ is a unit vector such that $\overrightarrow n.\overrightarrow u=\overrightarrow n.\overrightarrow v=0$, then $|\overrightarrow n.\overrightarrow w|=?$

asked Jan 13, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow v=2\hat i+\hat j-\hat k\:\:and\:\;\overrightarrow w=\hat i+3\hat k$ and $\overrightarrow u$ is a unit vector,then the maximum value of $ [\overrightarrow u\:\overrightarrow v\:\overrightarrow w]$ is ?

asked Jan 13, 2014 by rvidyagovindarajan_1

1 answer

If $ \overrightarrow r\times\overrightarrow b=\overrightarrow c\times\overrightarrow b$ and $\overrightarrow r.\overrightarrow a=0$, where $\overrightarrow a=2\hat i+3\hat j-\hat k,\:\overrightarrow b=3\hat i-\hat i+\hat k\:and\:\:\overrightarrow c=\hat i+\hat j+3\hat k$, then $\overrightarrow r=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=(-1,1,1)\:\:\overrightarrow b=(2,0,1)\:and\:\overrightarrow x$ is vector such that $\overrightarrow x.\overrightarrow a=7,\:\overrightarrow x.\overrightarrow b=0$ and $\overrightarrow a,\overrightarrow b,\overrightarrow x$ are coplanar, then $\overrightarrow x=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow c=\hat j-\hat k$ and $\overrightarrow b$ is such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow a.\overrightarrow b=3$ then $\overrightarrow b=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\;and\:\:\overrightarrow b=\hat i+\hat j$ and $\overrightarrow c$ is such that $\overrightarrow c.\overrightarrow a=|\overrightarrow c|$, $|\overrightarrow c-\overrightarrow a|=2\sqrt 2$ and the angle between $\overrightarrow a\times\overrightarrow b$ and $\overrightarrow c$ is $30^{\circ}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b$ are mutually $\perp$ unit vectors and the vectors $x\overrightarrow a+x\overrightarrow b+z(\overrightarrow a\times\overrightarrow b ),\:\:\overrightarrow a+(\overrightarrow a\times\overrightarrow b),\:\:and\:\:z\overrightarrow a+z\overrightarrow b+y(\overrightarrow a\times\overrightarrow b)$ lie in a plane then $Z$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are unit vectors and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ is also a unit vector and $\alpha,\beta,\gamma $ are angles between $\overrightarrow a\:and\:\overrightarrow b,\:\:\overrightarrow b\:and\:\overrightarrow c\:\:\overrightarrow c\:and\:\overrightarrow a$ respectively, then among the three angles,

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three coplanar vectors then, $[(2\overrightarrow a-\overrightarrow b)\:(2\overrightarrow b-\overrightarrow c)\:(2\overrightarrow c-\overrightarrow a)]=?$

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b$ are two non zero and non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$

asked Dec 17, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow {AB}=3\hat i-2\hat j+2\hat k$ and $\overrightarrow {BC}=-\hat i-2\hat k$ are adjacent sides of a parallelogram, then the angle between the diagonals is ?

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:and\:\overrightarrow b$ are two non collinear unit vectors and $\overrightarrow u=\overrightarrow a-(\overrightarrow a.\overrightarrow b)\overrightarrow b\:\:and\:\:\overrightarrow v=\overrightarrow a\times\overrightarrow b$, then $|\overrightarrow v|=?$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow v=2\hat i+\hat j-\hat k, \:\:and\:\:\overrightarrow w=\hat i+3\hat k\:\:and\:\:\overrightarrow u$ is a unit vector, then the maximum value of $[\overrightarrow u\:\overrightarrow v\:\overrightarrow w]=?$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=|\overrightarrow c|=1, \:|\overrightarrow b|=4,\:\overrightarrow a\times\overrightarrow b=2\overrightarrow a\times\overrightarrow c\:and\:$ if the angle between $\overrightarrow b\:and\:\:\overrightarrow c$ is $cos^{-1}\large\frac{1}{4}$ then $\overrightarrow b-2\overrightarrow c=?$

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

The number of vectors $\overrightarrow b$ of unit length which are $\perp$ to $\overrightarrow a=\hat i+2\hat j\:\:and\:\:\overrightarrow c=\hat j+2\hat k$ is?

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two unit vectors, then $\overrightarrow a\times\overrightarrow b$ is also a unit vector if ?

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

A man walks 4 mtrs. towards west and then walks 3 mtrs in the direction of $\large\frac{\pi}{6}\:$ radians east of north. What is the displacement of the man from the starting point?

asked Dec 5, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are any three unit vectors such that $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c=0$ and the angle between $\overrightarrow b\:\:and\:\:\overrightarrow c $ is $\large\frac{\pi}{6}$, then $\overrightarrow b\times\overrightarrow c=?$

asked Dec 5, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are any three vectors such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow b\times\overrightarrow c=\overrightarrow a$, then the magnitude of $\overrightarrow b$ is?

asked Dec 5, 2013 by rvidyagovindarajan_1

1 answer

$|\overrightarrow a\times\overrightarrow b|^2= ?$ (which one of the following )

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\overrightarrow b=\hat i\:\:and\:\:\overrightarrow c=x\hat i-\hat j+\hat k$, then the value of $x$ for which $\overrightarrow a\:\overrightarrow b\:and\:\overrightarrow c$ are coplanar is ?

asked Dec 1, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a= x^2\hat i+2\hat j-2\hat k,\:\overrightarrow b=\hat i-\hat j+\hat k\;and\:\overrightarrow c=x^2\hat i+5\hat j-4\hat k$ are three vectors, then the values of $x$ for which the angle between $\overrightarrow a\:and\:\overrightarrow b$ is acute and that between $\overrightarrow b\:and\:\overrightarrow c$ is obtuse is ?

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b\:and\:\overrightarrow c$ are non coplanar vectors and if $\overrightarrow a'=\large\frac{\overrightarrow b\times \overrightarrow c}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\overrightarrow b'=\large\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:and \:\overrightarrow c'=\large\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},$ then $\overrightarrow a.\overrightarrow a'+\overrightarrow b.\overrightarrow b'+\overrightarrow c.\overrightarrow c'=?$

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

For any vector $\overrightarrow a\:\:and\:\:\overrightarrow b$ the angle between $|\overrightarrow a|\overrightarrow b+|\overrightarrow b|\overrightarrow a$ and $|\overrightarrow a|\overrightarrow b-|\overrightarrow b|\overrightarrow a$ is ?

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

The value of $a$ for which the volume of the parallelopiped formed by the vectors $\hat i+a\hat j+\hat k,\:\:\hat j+a\hat k,\:\:a\hat i+\hat k$ is minimum is ?

asked Nov 28, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c$ and $\overrightarrow a\times\overrightarrow b=\overrightarrow a\times\overrightarrow c$ and if $\overrightarrow a\neq 0$, then

asked Nov 21, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors then $(\overrightarrow a+\overrightarrow b+\overrightarrow c).(\overrightarrow b+\overrightarrow c)\times (\overrightarrow c+\overrightarrow a)=?$

asked Nov 21, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two non zero non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j,\:\:\overrightarrow b=2\hat j-\hat k$ and $\overrightarrow r\times \overrightarrow a=\overrightarrow b\times\overrightarrow a,\:\:\overrightarrow r\times\overrightarrow b=\overrightarrow a\times\overrightarrow b$ then a unit vector in the direction of $\overrightarrow r$ is ?

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit non collinear vectors and if $\overrightarrow u=\overrightarrow a-(\overrightarrow a.\overrightarrow b)\overrightarrow b$ and $\overrightarrow v=\overrightarrow a\times\overrightarrow b$ then $ |\overrightarrow v|= ?$

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j.$ and $\overrightarrow c$ is a vector such that $\overrightarrow a.\overrightarrow c=|\overrightarrow c|,\:\:|\overrightarrow c-\overrightarrow a|=2\sqrt 2 $ and angle between $\overrightarrow a\times\overrightarrow b\:\:and\:\:\overrightarrow c$ is $\large\frac{\pi}{6}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=2\hat i+3\hat j-\hat k\:\:and\:\:\overrightarrow b=\hat i-2\hat j+3\hat k$, then the value of $\lambda$ for which $\overrightarrow c=\lambda\hat i+\hat j+(2\lambda+1)\hat k$ is parallel to the plane containing $\overrightarrow a\:\:and\:\:\overrightarrow b$ is

asked Nov 15, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b\:\overrightarrow c$ are three vectors of equal magnitude and angle between $\overrightarrow a\:and\:\overrightarrow b$ is $\alpha$, that between $\overrightarrow b\:\overrightarrow c$ is $\beta$, and that between $\overrightarrow a\:and\:\overrightarrow c$ is $\gamma$ then the minimum value of $cos\alpha+cos\beta+cos\gamma$ is ?

asked Nov 15, 2013 by rvidyagovindarajan_1

1 answer

If $a,b,c$ are lengths of sides of a $\Delta\:ABC$ and for any non collinear vectors $\overrightarrow u\:\:and\:\:\overrightarrow v$ if $(a-b)\overrightarrow u+(b-c)\overrightarrow v+(c-a)(\overrightarrow u\times\overrightarrow v)=0$, then the $\Delta$ is ?

asked Nov 13, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k\:\:\overrightarrow b=4\hat i+3\hat j+4\hat k\:\:and\:\:\overrightarrow c=\hat i+\alpha\hat j+\beta\hat k$ are linear dependent vectors and $|\overrightarrow c|=\sqrt 3$ then $ (\alpha,\beta)=?$

asked Nov 12, 2013 by rvidyagovindarajan_1

1 answer

The value of $a$ for which the volume of the parallelopiped formed by vectors $\hat i+a\hat j+\hat k,\:\:\hat j+a\hat k\:\:and\:\: a\hat i+\hat k$ becomes minimum is ?

asked Nov 12, 2013 by rvidyagovindarajan_1

1 answer

If $ \overrightarrow x=\large\frac{\overrightarrow b\times\overrightarrow c}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\:\overrightarrow y=\large\frac{\overrightarrow c\times\overrightarrow a}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\:and\:\:\overrightarrow z=\large\frac{\overrightarrow a\times\overrightarrow b}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},$ then $\overrightarrow x.(\overrightarrow a+\overrightarrow b)+\overrightarrow y.(\overrightarrow b+\overrightarrow c)+\overrightarrow z.(\overrightarrow c+\overrightarrow a)=?$

asked Nov 12, 2013 by rvidyagovindarajan_1

1 answer

For non zero vectors $\overrightarrow a,\overrightarrow b\:and\:\overrightarrow c,\:\:if\:\:|(\overrightarrow a\times\overrightarrow b).\overrightarrow c|=|\overrightarrow a||\overrightarrow b||\overrightarrow c|$ then ?

asked Nov 11, 2013 by rvidyagovindarajan_1

1 answer

If $a,b,c$ are non negative and distinct numbers and vectors $a\hat i+a\hat j+c\hat k,\:\:\hat i+\hat k\:\:and\:\:c\hat i+c\hat j+b\hat k$ lie in a plane then c is ?

asked Nov 11, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow a.\overrightarrow b=1$ and $\overrightarrow a\times\overrightarrow b=\hat j-\hat k,$ then $\overrightarrow b=?$

asked Nov 10, 2013 by rvidyagovindarajan_1

1 answer

For any vector $\overrightarrow a$ the value of $(\overrightarrow a\times \hat i)^2+(\overrightarrow a\times \hat j)^2+(\overrightarrow a\times \hat i)^2=?$

asked Nov 10, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+2\hat j+\hat k,\:\overrightarrow b=\hat i-\hat j+\hat k$ and $\overrightarrow c=\hat i+\hat j-\hat k$ and a vector $\overrightarrow d$ which is in the plane of $\overrightarrow a\:and\:\overrightarrow b$ and whose projection on $\overrightarrow c$ is $\large\frac{1}{\sqrt 3}, $ then $\overrightarrow d=?$

asked Nov 10, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a, \:\overrightarrow b,\: \overrightarrow c$ are position vectors of the points $A,B,C$ respectively, then under what condition the three points $A,B,C$ are collinear?

asked Nov 10, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow {OA}=\overrightarrow a,\:\overrightarrow {AB}=6\overrightarrow a+2\overrightarrow b\:and\:\overrightarrow {OC}=\overrightarrow b$, $p$ is area of quadrateral $OACB$ and $q$ is area of parallelogram with $OA$ and $OC$ as adjacent sides, and if $p=x.q$, then $x=?$

asked Nov 8, 2013 by rvidyagovindarajan_1

1 answer

The vector that makes equal angle with $\large\frac{1}{3}$$(\hat i-2\hat j+2\hat k), \:\large\frac{1}{5}$$(-4\hat i-3\hat k)$ and $\hat j$ is ?

asked Nov 7, 2013 by rvidyagovindarajan_1

1 answer

The set of all possible values of $'c'$ for which $\overrightarrow a=c \log_3 x\hat i-6\hat j+3\hat k$ and $\overrightarrow b=\log_3x\hat i+2\hat j+2c\log_3x\hat k$ making acute angle for $\forall x\in (0,\infty)$ is ?

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

In a rt. angled $\Delta$ $ABC$, the hypotenuse $|\overrightarrow {AB}|=p$,then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}=?$

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

Area of a parallelogram with adjacent sides $\overrightarrow a=\overrightarrow p+2\overrightarrow q,$ and $\overrightarrow b=2\overrightarrow p+\overrightarrow q$, where $\overrightarrow p,\overrightarrow q$ are unit vectors with angle $\large\frac{\pi}{6}$ between them is ?

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

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