No Author Solutions for Exercise 1: EXERCISE

If from a point $P\left(a,b,c\right)$ perpendiculars $PA, PB$ are drawn to $YZ$and $ZX$ planes, then the equation of the plane $OAB$ is

The equation of the planes through the intersection of the planes $x+3y+6=0$ and $3x-y-4z=0,$ whose perpendicular distance from the origin is unity, are

Let $P_1$ denotes the equation of a plane to which the vector $\left(\hat{i}+\hat{j}\right)$ is normal, and which contains the line $L$ whose equation is $\overrightarrow{r}=\hat{i}+\hat{j}+\hat{k}+\lambda \left(\hat{i}-\hat{j}-\hat{k}\right)$ and $P_2$ denotes the equation of the plane containing the line $L$ and a point with position vector $\hat{j}.$ Which of the following holds good?

The vector $\overrightarrow{c}$ directed along the internal bisector of the angle between the vectors $a=7\hat{i}-4\hat{j}-4\hat{k}$ and $b=-2\hat{i}-\hat{j}+2\hat{k}$ with $\left|\overrightarrow{c}\right|=5\sqrt{6}$ is

For three non-zero vectors $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}, \left|\left(\overrightarrow{a}\times \overrightarrow{b}\right)·\overrightarrow{c}\right|=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\left|\overrightarrow{c}\right|$ holds if and only if

If $\hat{a}$ and $\hat{b}$ are unit vectors, then the greatest value of $\left|\hat{a}+\hat{b}\right|+\left|\hat{a}-\hat{b}\right|$ is

Let the unit vectors $\hat{a}$ and $\hat{b}$ be perpendicular to each other and the unit vector $\hat{c}$ be inclined at an angle $\theta$ to both $\hat{a}$ and $\hat{b}$ If $\hat{c}=x\hat{a}+y\hat{b}+z\left(\hat{a}\times \hat{b}\right),$ then

If $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ are non-coplanar vectors and $\lambda$ is a real number, then $\left[\lambda (\overrightarrow{a}+\overrightarrow{b}) {\lambda }^2\overrightarrow{b} \lambda \overrightarrow{c}\right]=[\overrightarrow{a} \overrightarrow{b}+\overrightarrow{c} \overrightarrow{b}]$ for