The value of \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}\) is

A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to

The vectors \(\overrightarrow{a}-\overrightarrow{b},\overrightarrow{b}-\overrightarrow{c},\overrightarrow{c}-\overrightarrow{a}\) are

If \(\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}\) are the position vectors of three collinear points, then which of the following is true?

If \(\lambda \hat{i}+2\lambda \hat{j}+2\lambda \hat{k}\) is a unit vector, then the value of \(\lambda\) is

Represent graphically the displacement of 80km, 60° south of west.

Find the direction cosines of a vector whose direction ratios are 2, 3, - 6.

Find the direction cosines of \(\overrightarrow{AB},\) where A is (2, 3, 1) and B is (3, - 1, 2).

Show that the points whose position vectors are 2\(\hat{i}\) + 3\(\hat{j}\) − 5\(\hat{k}\), 3\(\hat{i}\) + \(\hat{j}\) − 2\(\hat{k}\) and, 6\(\hat{i}\) − 5\(\hat{j}\) + 7\(\hat{k}\) are collinear

If \(\overrightarrow{a},\overrightarrow{b},\)and \(\overrightarrow{c}\) are three unit vectors satisfying  \(\overrightarrow{a}-\sqrt{3}\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}\)  then find the angle between \(\overrightarrow{a}\) and \(\overrightarrow{c}\).

Find the unit vector in the direction of the vector \(\overrightarrow { a } -2\overrightarrow { b } +3\overrightarrow { c } \) if \(\overrightarrow { a } =\hat { i } +\hat { j } ,\overrightarrow { b } =\hat { j } +\hat { k } \) and \(\overrightarrow { c } =\hat { i } +\hat { k } \) .

If \(\overrightarrow{a},\overrightarrow{b}\) are unit vectors and \(\theta\) is the angle between them, show that \(sin {\theta \over 2}={1\over2}|\overrightarrow{a}-\overrightarrow{b}|\)