Recent questions in Vector Algebra

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

$|\overrightarrow a|=3,\:|\overrightarrow b|=4,\:|\overrightarrow a+\overrightarrow b|=5,$ then $|\overrightarrow a-\overrightarrow b|=?$

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i-\hat j+2\hat k, \:\:\overrightarrow b=2\hat i+4\hat j+\hat k\:\:and\:\:\overrightarrow c=\lambda \hat i+\hat j+\mu k$ are mutually $\perp$ then $(\lambda,\mu)=?$

asked Nov 5, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\;and\:\overrightarrow b$ are unit vectors and if vectors $\overrightarrow c=\overrightarrow a+2\overrightarrow b$ and $\overrightarrow d=5\overrightarrow a-4\overrightarrow b$ are $\perp$ to each other, then the angle between $\overrightarrow a\;and\:\overrightarrow b$ is ?

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a$ and $\overrightarrow b$ are such that $|\overrightarrow a+\overrightarrow b|=\sqrt {29}$ 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 the possible value of $(\overrightarrow a+\overrightarrow b).(-7\hat i+2\hat j+3\hat k)=?$

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

The vector $\hat i+x\hat j+3\hat k$ is rotated about angle $\theta$ and is doubled in magnitude, then it becomes $4\hat i+(4x-2)\hat j+2\hat k$ . The value of $x=?$

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i-\hat k,\:\overrightarrow b=x\hat i+\hat j+(1-x)\hat k\:and\:\overrightarrow c=y\hat i+x\hat j+(1+x-y)\hat k$ , then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$ depends on?

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i-\hat k,\:\overrightarrow b=x\hat i+\hat j+(1-x)\hat k\:and\:\overrightarrow c=y\hat i+x\hat j+(1+x-y)\hat k$ , then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$ depends on?

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors and $\theta$ is angle between them then $\large\frac{1}{2}$ $|\overrightarrow a-\overrightarrow b|$ =?

asked Nov 1, 2013 by rvidyagovindarajan_1

1 answer

$(\overrightarrow a+\overrightarrow b+\overrightarrow c).[(\overrightarrow a+\overrightarrow b)\times (\overrightarrow a+\overrightarrow c)]=?$

asked Nov 1, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow p,\overrightarrow q$ are non collinear vectors, then $[\hat i\:\overrightarrow p\:\overrightarrow q]\hat i+[\hat j\:\overrightarrow p\:\overrightarrow q]\hat j+[\hat k\:\overrightarrow p\:\overrightarrow q]\hat k$ =?

asked Nov 1, 2013 by rvidyagovindarajan_1

1 answer

The angle between the diagonals of a parallelogram $ABCD$ , where $\overrightarrow {AB}=3\hat i-2\hat j+2\hat k$ and $\overrightarrow {BC}=-\hat i-2\hat k$ is?

asked Nov 1, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=2,\:|\overrightarrow b|=3\:and\:|\overrightarrow c|=4$ and $\overrightarrow a+\overrightarrow b+\overrightarrow c=\overrightarrow O$ , then $\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a+\overrightarrow a.\overrightarrow b=?$

asked Oct 30, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b\:and\:\overrightarrow c$ are mutually $\perp$ vectors of equal magnitude then the angle $\theta$ made by $\overrightarrow a+\overrightarrow b+\overrightarrow c$ with any one of these 3 vectors is ?

asked Oct 30, 2013 by rvidyagovindarajan_1

1 answer

The sides of a parallelogram are given by vectors $2\hat i+4\hat j-5\hat k$ and $\hat i+2\hat j+3\hat k$ . Unit vector along one of the diagonals is given by ?

asked Oct 30, 2013 by rvidyagovindarajan_1

1 answer

The points with position vectors $60\hat i+3\hat j,\:70\hat i-8\hat j\:and\:a\hat i-52\hat j$ are collinear if $a=?$

asked Oct 29, 2013 by rvidyagovindarajan_1

1 answer

$[\overrightarrow a\:\:\overrightarrow b\:\:\overrightarrow a\times\overrightarrow b]$ =?

asked Oct 29, 2013 by rvidyagovindarajan_1

1 answer