Vector Algebra - Algebra - Mathematics Previous Year Questions

If a and b are vectors such that \(|a + b|=|a-b|\), then the angle between a and b is

If \(a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j - \widehat k\), then a vector perpendicular to a and in the plane containing b and c is

OA and BO are two vectors of magnitudes 5 and 6 respectively. If \(\angle BOA=60^\circ\), then OA . OB is equal to

If |a| = 8, |b| = 3 and |a \(\times\) b| = 12, then find the angle between a and b.

The vector that must be added to \(\widehat i - 3\widehat j + 2\widehat k\) and \(3\widehat i + 6\widehat j - 7\widehat k\) so resultant vector is a unit vector along the X-axis is

If for \(a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k\) and \(c = - 3\widehat i + \widehat j + 2\widehat k\), then find \([a\,b\,c]\).

If \(\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}\) and \(\mathbf{r}=\hat{i}+\hat{k}\), then the unit vector in the direction of \(3 p+q-2 r\) is

If x, y and z are non-zero real numbers and \(a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k\) and \(c = x\widehat i + y\widehat j + z\widehat k\) are such that \(a \times b = z\widehat i - 3\widehat j + \widehat k\), then [a b c] is equal to

If \(\theta\) be the angle between the vectors \(a = 2\widehat i + 2\widehat j - \widehat k\) and \(b = 6\widehat i - 3\widehat j + 2\widehat k\), then

The scalar components of a unit vector which is perpendicular to each of the vectors \(\hat{\imath}+2 \hat{\jmath}-\hat{k}\) and \(3 \hat{\imath}-\hat{\jmath}+2 \hat{k}\) are

$$\text { If } \vec{a} \text { and } \vec{b} \text { are unit vectors, then the angle between } \vec{a} \text { and } \vec{b} \text { for which } a-\sqrt{2} \vec{b} \text { is a unit vector is }$$

$$\text { The angle between } \hat{\imath}-\hat{\jmath} ~\&~ \hat{\jmath}-\hat{k} \text { is }$$

Let a, b, c be three vector such that \(a \neq 0\) and \(\vec{a} \times \vec{b}=2 \vec{a} \times \vec{c},|a|=|c|=1,|b|=4\) and \(|\vec{b} \times \vec{c}|=\sqrt{15}\). If \(\vec{b}-2 \vec{c}=\lambda \vec{a}\) then \(\lambda\) equals to

Find the value of '\(b\)' such that the scalar product of the vector \(\hat{\imath}+\hat{\jmath}+\hat{k}\) with the unit vector parallel to the sum of the vectors \(2 \hat{\imath}+4 \hat{\jmath}-5 \hat{k}\) and \(b \hat{\imath}+2 \hat{\jmath}+3 \hat{k}\) is unity

$$\text { If } \hat{\imath}+\hat{\jmath}-\hat{k} \quad \&~ 2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \text { are adjacent sides of a parallelogram, then length of its diagonals are }$$

The vector \((\vec{r})\) whose magnitude is \(3 \sqrt{2}\) units which makes an angle of \(\frac{\pi}{4}\) and \(\frac{\pi}{2}\) with \(y\) and \(z\)- axis respectively is

$$\text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|=$$