Vector Algebra

The direction ratios of the vector $\hat{k}$ are:

If $\vec{a}$ is a vector, then $|-\vec{a}|$ is equal to:

The magnitude of the vector $\sqrt{2}\hat{i} + \sqrt{2}\hat{j}$ is:

What are the projections of the vector $\vec{a} = 2\hat{i} + 3\hat{j} + 6\hat{k}$ on the coordinate axes?

A point $P$ is at a distance of $1$ unit from the origin. If the line $OP$ makes an angle of $45^\circ$ with both the $x$ and $y$ axes and $90^\circ$ with the $z$ axis, the coordinates of $P$ are:

The direction ratios of the line $\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$ are:

The vector components of $\vec{r} = -2\hat{i} + 4\hat{k}$ are:

Which of the following describes the vector $\hat{i} - \hat{i}$?

If $\vec{a}$ is a vector of magnitude 5, then the magnitude of $-3\vec{a}$ is:

If $\vec{a} = 2\hat{i} - \hat{j}$, then the magnitude of the vector $3\vec{a}$ is:

The magnitude of the vector $\hat{i} + \hat{j} + \hat{k}$ is:

Two vectors are said to be equal if they have:

Calculate the dot product of $\hat{i} - 2\hat{j} + \hat{k}$ and $\hat{i} + \hat{j} + \hat{k}$.

Find the value of $3\hat{k} \cdot 2\hat{k}$.

Find $\vec{a} \cdot \vec{b}$ if $\vec{a} = \hat{i} + \hat{k}$ and $\vec{b} = \hat{i} - \hat{k}$.

If $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ for a non-zero vector $\vec{a}$, then:

The vector product of two non-zero vectors is always a:

What is the magnitude of $\hat{i} \times \hat{k}$?