List of top Mathematics Questions on Vectors asked in CBSE CLASS XII

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ such that $|\vec{a}| = 3$, $|\vec{b}| = 5$, $|\vec{c}| = 7$, then find the angle between $\vec{a}$ and $\vec{b}$.

Let $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ be three vectors such that $\mathbf{a} \times \mathbf{b} = \mathbf{a} \times \mathbf{c} \text{ and } \mathbf{a} \times \mathbf{b} \neq 0 \text{ Show that } \mathbf{b} = \mathbf{c}$.

Find a vector of magnitude 5 which is perpendicular to both the vectors $ 3\hat{i} - 2\hat{j} + \hat{k} \text{ and } 4\hat{i} + 3\hat{j} - 2\hat{k} $.

The unit vector perpendicular to the vectors $ \hat{i} - \hat{j} $ and $ \hat{i} + \hat{j} $ is:

If $ \vec{\alpha} = \hat{i} - 4 \hat{j} + 9 \hat{k} $ and $ \vec{\beta} = 2\hat{i} - \hat{j} + \lambda \hat{k} $ are two mutually parallel vectors, then $ \lambda $ is equal to:

During a cricket match, the position of the bowler, the wicket keeper and the leg slip fielder are in a line given by $ \vec{B} = 2\hat{i} + \hat{j} $, $ \vec{W} = 6\hat{i} + 12\hat{j} $ and $ \vec{F} = 12\hat{i} + 1\hat{j} $ respectively. Calculate the ratio in which the wicketkeeper divides the line segment joining the bowler and the leg slip fielder.

Let $ \vec{p} $ and $ \vec{q} $ be two unit vectors and $ \alpha $ be the angle between them. Then $ (\vec{p} + \vec{q}) $ will be a unit vector for what value of $ \alpha $?

If $ \mathbf{a} $ and $ \mathbf{b} $ are position vectors of two points $ P $ and $ Q $ respectively, then find the position vector of a point $ R $ in $ QP $ produced such that \[ QR = \frac{3}{2} QP. \]

If $ |\mathbf{a}| = 2 $, $ |\mathbf{b}| = 3 $ and $ \mathbf{a} \cdot \mathbf{b} = 4 $, then evaluate $ |\mathbf{a} + 2\mathbf{b}| $.

If the projection of $ \mathbf{a} = \alpha \hat{i} + \hat{j} + 4 \hat{k} $ on $ \mathbf{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} $ is 4 units, then $ \alpha $ is:

Let $ \vec{p} = 2\hat{i} - 3\hat{j} - \hat{k} $, $ \vec{q} = -3\hat{i} + 4\hat{j} + \hat{k} $ and $ \vec{r} = \hat{i} + \hat{j} + 2\hat{k} $. Express $ \vec{r} $ in the form of $ \vec{r} = \lambda \vec{p} + \mu \vec{q} $ and hence find the values of $ \lambda $ and $ \mu $.

What is the projection of vector $ \overrightarrow{DV} $ on vector $ \overrightarrow{DA} $?

Find the measure of $ \angle VDA $.

Find a unit vector in the direction of $ \overrightarrow{DA} $.

How far is the star $ V $ from star $ A $?

If $ \vec{a} $ and $ \vec{b} $ are two vectors such that $ |\vec{a}| = 1 $, $ |\vec{b}| = 2 $, and $ \vec{a} \cdot \vec{b} = \sqrt{3} $, then the angle between $ 2\vec{a} $ and $ -\vec{b} $ is:

Let $ \vec{a} $ be any vector such that $ |\vec{a}| = a $. The value of $ |\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2 $ is:

The vectors $ \vec{a} = 2\hat{i} - \hat{j} + \hat{k} $, $ \vec{b} = \hat{i} - 3\hat{j} - 5\hat{k} $, and $ \vec{c} = -3\hat{i} + 4\hat{j} + 4\hat{k} $ represent the sides of:

A vector perpendicular to the line $ \vec{r} = \hat{i} + \hat{j} - \hat{k} + \lambda (3\hat{i} - \hat{j}) $ is: