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Questions >> JEEMAIN and NEET >> Mathematics >> Class12 >> Vector Algebra

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

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If vector $\overrightarrow a$ is unit vector and it makes angle $\large\frac{\pi}{4}$ with $\hat k$ and $\overrightarrow a+\hat i+\hat j$ is also a unit vector, then $\overrightarrow a=?$

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If $D\:\:and\:\:E$ are mid points of the side $\overline {AB}\:\:and\:\:\overline {AC}$ of a $\Delta \:ABC$ , then $\overrightarrow {BE}+\overrightarrow {DC}=?$

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If sum of two unit vectors is also a unit vector then the magnitude of their difference is ?

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow {AB}=3\hat i+\hat j-2\hat k,\:and \:\overrightarrow {AC}=-\hat i+3\hat j+4\hat k$ are two sides af the $\Delta ABC$ , then the length of the median through $A$ is ?

asked Dec 1, 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 $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are three vectors of magnitude $3,4,5$ respectively. If each vector is $\perp$ to sum of the other two vectors then $|\overrightarrow a+\overrightarrow b+\overrightarrow c|=?$

asked Nov 30, 2013 by rvidyagovindarajan_1

1 answer

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is ?

asked Nov 30, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a+\overrightarrow b|=|\overrightarrow a|$ , then the angle between $2\overrightarrow a+\overrightarrow b$ and $\overrightarrow b$ is ?

asked Nov 29, 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

If the vectors $p\hat i+\hat j+\hat k,\:\hat i+q\hat j+\hat k,\: \:and\:\:\hat i+\hat j+r\hat k$ $(p\neq q\neq r\neq 1)$ are three coplanar vectors then the value of $pqr-(p+q+r)=?$

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

asked Nov 28, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are non coplanar vectors and $p,q$ are real numbers so that $[3\overrightarrow u\:p\overrightarrow v\:p\overrightarrow w]-[p\overrightarrow v\:p\overrightarrow w\:q\overrightarrow u]-[2\overrightarrow w\:q\overrightarrow v\:q\overrightarrow u]=0$ then number of values of $p,q$ is

asked Nov 22, 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 $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors, then $[\overrightarrow a+\overrightarrow b+\overrightarrow c\:\overrightarrow a-\overrightarrow c\:\overrightarrow a-\overrightarrow b]=?$

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 $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are non zero, non collinear vectors such that $\overrightarrow a\times\overrightarrow b=\overrightarrow b\times\overrightarrow c=\overrightarrow c\times\overrightarrow a$ , then $\overrightarrow a+\overrightarrow b+\overrightarrow c=?$

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

If the magnitude of the vector $a\hat i+b\hat j+c\hat k$ is $|a|+|b|+|c|$ , then $a,b,c$ should be ?

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:and\:\overrightarrow c$ are unit and collinear vectors and $|\overrightarrow b|=6$ , then $\overrightarrow b-3\overrightarrow c=\lambda \overrightarrow a,$ if $\lambda=?$

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=|\overrightarrow b|=1$ and $|\overrightarrow a+\overrightarrow b|=\sqrt 3$ and $\overrightarrow c$ is such that $\overrightarrow c-\overrightarrow a-2\overrightarrow b=3(\overrightarrow a\times\overrightarrow b)$ , then $\overrightarrow c.\overrightarrow b=?$

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=5, \:|\overrightarrow b|=3\:|\overrightarrow c|=4$ and $\overrightarrow a$ is $\perp$ to $\overrightarrow b\:\:and\:\:\overrightarrow c$ then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=?$

asked Nov 18, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are three vectors such that $|\overrightarrow u|=1,\:|\overrightarrow v|=2,\:|\overrightarrow w|=3$ and if the projection of $\overrightarrow v$ along $\overrightarrow u$ is equal to that of $\overrightarrow w$ along $\overrightarrow u$ and also if $\overrightarrow u$ and $\overrightarrow v$ are $\perp$ to each other, then $|\overrightarrow u-\overrightarrow v+\overrightarrow w|= ?$

asked Nov 18, 2013 by rvidyagovindarajan_1

1 answer

The value of $[\overrightarrow a-\overrightarrow b\:\:\overrightarrow b-\overrightarrow c\:\:\overrightarrow c-\overrightarrow a]$ where $|\overrightarrow a|=1,\:\:|\overrightarrow b|=5\:\:|\overrightarrow c|=3$ is ?

asked Nov 18, 2013 by rvidyagovindarajan_1

1 answer

The greatest value of $|\overrightarrow a+\overrightarrow b|+|\overrightarrow a-\overrightarrow b|$ where $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors is ?

asked Nov 18, 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 $\overrightarrow {OA}=\hat i+3\hat j-2\hat k\:\:and\:\:\overrightarrow {OB}=3\hat i+\hat j-2\hat k$ and $\overrightarrow {OC}$ is angular bisector of angle $AOB$ with $C$ being the point on the line $AB$ , then $\overrightarrow {OC}=?$

asked Nov 13, 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

If $\overrightarrow a,\overrightarrow b\:\:and\:\:\overrightarrow c$ are non coplanar vectors, then for real $\lambda$ , $[\lambda(\overrightarrow a+\overrightarrow b)\:\lambda^2\overrightarrow b\:\lambda\overrightarrow c]=[\overrightarrow a\:\overrightarrow b+\overrightarrow c\:\overrightarrow c]$ , for:

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 $\overrightarrow a,\overrightarrow b\:and\:\overrightarrow c$ are non zero vectors that are pair wise non-collinear and if $\overrightarrow a+3\overrightarrow b$ is collinear with $\overrightarrow c$ and $\overrightarrow b+2\overrightarrow c$ is collinear with $\overrightarrow a$ , then $\overrightarrow a+3\overrightarrow b+6\overrightarrow c=?$

asked Nov 9, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a+\overrightarrow b|=\sqrt {29}$ and $\overrightarrow a\times (2\hat i+3\hat j+4\hat k)=(2\hat i+3\hat j+4\hat k)\times \overrightarrow b,$ then $(\overrightarrow a+\overrightarrow b).(-7\hat i+2\hat j+3\hat k)=?$

asked Nov 9, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=3,\:|\overrightarrow b|=\large\frac{\sqrt 2}{3}$ , then $\overrightarrow a\times\overrightarrow b$ is a unit vector if the angle between $\overrightarrow a$ and $\overrightarrow b$ is ?

asked Nov 8, 2013 by rvidyagovindarajan_1

1 answer

The number of distinct real values of $\lambda$ for which the vectors $-\lambda^2\hat i+\hat j+\hat k,\:\hat i-\lambda^2\hat j+\hat k\:and\:\hat i+\hat k-\lambda^2 \hat k$ are coplanar is?

asked Nov 8, 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

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