Vector Algebra

If $|\mathbf{a}+\mathbf{b}|=|\mathbf{a}-\mathbf{b}|$, then $\mathbf{a}$ and $\mathbf{b}$ are

The work done by the force $4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ in moving a particle along a straight line from the point $(3,2,-1)$ to $(2,-1,4)$ is

The number of vectors of unit length perpendicular to vectors $\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}$ and $\mathbf{b}=\hat{\mathbf{j}}+\hat{\mathbf{k}}$, is

The value of $|\vec{a} \times \vec{b}+\vec{b} \times \vec{a}|$ is

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are any three mutually perpendicular vectors of equal magnitude $a$, then $|\mathbf{a}+\mathbf{b}+\mathbf{c}|$

Given three vectors $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ each two of which are non collinear. Further if $(a+b)$ is collinear with $\mathbf{c}$, $(\mathbf{b}+\mathbf{c})$ is collinear with $\mathbf{a}$ and…

The value of $\left\{(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})^2+(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2\right\} \div a^2 b^2$ is

A parallelogram is constructed on the vectors $\overrightarrow{\mathrm{a}}=3 \vec{\alpha}-\vec{\beta}, \vec{b}=\vec{\alpha}+3 \vec{\beta}$. If $|\vec{\alpha}|=|\vec{\beta}|=2$ and the angle between $\vec{\alpha}$ and…

A parallelogram is constructed on the vectors $\mathbf{a}=3 \alpha-\beta, \mathbf{b}=\alpha+3 \beta$. If $|\alpha|=|\beta|=2$ and the angle between $\alpha$ and $\beta$ is $\frac{\pi}{3}$, then length of a diagonal of…

The area of a parallelogram with diagonals as $\mathbf{a}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ is

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are non-collinear vectors such that for some scalars, $x, y, z$, $x \mathbf{a}+x \mathbf{b}+x \mathbf{c}=0$, then

$\overrightarrow{\mathbf{a}}=\frac{1}{7}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}), \overrightarrow{\mathbf{b}}=\frac{1}{7}(3 \hat{\mathbf{i}}-\lambda \hat{\mathbf{j}}+2 \hat{\mathbf{k}})$. If…