The acute angle between the planes $\mathrm{P}_1$ and $\mathrm{P}_2$, when $\mathrm{P}_1$ and $\mathrm{P}_2$ are the planes passing through the intersection of the planes $...

If two distinct point $Q, R$ lie on the line of intersection of the planes $-x+2 y-z=0$ and $3 x-5 y+2 z=0$ and $...

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$. Then the number of vectors $\overrightarrow{\mathrm{b}}$ such that $\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}$ and $|\overrightarrow{\mathrm{b}}| \in\{1,2, \ldots \ldots, 10\}$ is

If two straight lines whose direction cosines are given by the relations $I+m-n=0,3 I^2+m^2+c n l=0$ are parallel, then the positive value of $c$ is:

Let $\vec{a}=\alpha \hat{i}+3 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}-\beta \hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+2 \hat{j}-2 \hat{k}$ where $\alpha, \beta \in R$, be three vectors. If the projection of $\vec{a}$...

If $\vec{a} \cdot \vec{b}=1, \vec{b} \cdot \vec{c}=2$ and $\vec{c} \cdot \vec{a}=3$, then the value of $...