CUET Mathematics Mock Test - 1

If the angle between $\vec{a}$ and $\vec{b}$ is $\frac{2\pi }{3}$ and the projection of $\vec{a}$ in the direction of $\vec{b}$ is $-2$, then $|\vec{a}|$ is:

Let $L_1$ and $L_2$ be two parallel lines with the equations $\vec{r}={\vec{a}}_1+\lambda \vec{b}$ and $\vec{r}={\vec{a}}_2+\mu \vec{b}$ respectively. The shortest distance between them is:

What is the perpendicular distance from the point $(2,3,4)$ to the line $\frac{x-0}{1}=\frac{y-0}{0}=\frac{z-0}{0}$?

Find the angle between the line $\vec{r}=(\hat{i}+2\hat{j}-\hat{k})+\lambda (\hat{i}-\hat{j}+\hat{k})$ and the plane $\vec{r}\cdot (2\hat{i}-\hat{j}+\hat{k})=6$.

Consider the constraints:$5x+y\le 100$$x+y\le 60$$x\ge 0,y\ge 0$ Solving by graphical method, which point among the following will not form a boundary/corner point of the feasible region?