Dot product

Match the statements given in Column I with the values given in Column II

Let P, Q, R and S be the points on the plane with position vectors $-2\hat i-\hat j$, $4\hat i$, $3\hat i+3\hat j$ and $-3\hat i+2\hat j$ respectively. The quadrilateral PQRS must be a

Two adjacent sides of a parallelogram ABCD are given by $\overrightarrow{AB}=2\hat i+10\hat j+11\hat k$ and $\overrightarrow{AD}=-\hat i+2\hat j+2\hat k$.

The side AD is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that AD becomes AD′. If AD′ makes a right angle with the side AB, then the cosine of the angle $\alpha$ is given by

Match the statements in Column-I with the values in Column-II.

Match the statements/expressions given in Column I with the values given in Column II.

Let two non-collinear unit vectors $\hat a$ and $\hat b$ form an acute angle. A point $P$ moves so that at any time $t$ the position vector $\overrightarrow{OP}$ (where $O$ is the origin) is given by $\hat a\cos t+\hat b\sin t$. When $P$ is farthest from origin $O$, let $M$ be the length of $\overrightarrow{OP}$ and $\hat u$ be the unit vector along $\overrightarrow{OP}$. Then,