Vector Algebra - Algebra - Mathematics Previous Year Questions

If \(a = - \widehat i + \widehat j + \widehat k\) and \(b = 2\widehat i + \widehat k\), then find z component of a vector r, which is coplanar with a and b, r . b = 0 and r . a = 7.

If a and b are two vectors such that | a | = 1, | b | = 4 a . b = 2. If c = (2a \(\times\) b) \(-\) 3b, then angle between b and c

For non-zero vectors a, b, c; |(a \(\times\) b) . c| = |a| |b| |c| holds if and only if

Let a, b, c be vectors of lengths 3, 4, 5 respectively and a be perpendicular to (b + c), b to (c + a) and c to (a + b), then the value of (a + b + c) is

The points with position vectors \(10\widehat i + 3\widehat j\), \(12\widehat i - 5\widehat j\) and \(a\widehat i + 11\widehat j\) are collinear, if a is

\(\widehat u\) and \(\widehat v\) are two non-collinear unit vectors such that \(\left| {{{\widehat u + \widehat v} \over 2} + \widehat u \times \widehat v} \right| = 1\). Then the value of \(|\widehat u \times \widehat v|\) is equal to

Let \(\mathbf{a}=2 \mathbf{i}+\mathbf{j}+\mathbf{k}, \mathbf{b}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}\) and \(a\) unit vector \(\mathbf{c}\) be coplanar. If \(\mathbf{c}\) is perpendicular to \(\mathbf{a}\), then c equals to

If $\mathbf{a , b , c}$ are vectors such that $|\mathbf{b}|=|\mathbf{c}|$ then $\{(\mathbf{a}+\mathbf{b}) \times(\mathbf{a}+\mathbf{c})\} \times(\mathbf{b} \times \mathbf{c}) \cdot(\mathbf{b}+\mathbf{c})$ is equal to