Vector Algebra — JEE Main PYQs

Let $\vec{a},\vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of these are collinear. If the vector $\vec{a}+2\vec{b}$ is collinear with $\vec{c}$ and $\vec{b}+3\vec{c}$ is collinear with $\vec{a}$ ( $\lambda$ being some non-zero scalar) then …

A particle is acted upon by constant forces $4\hat{i}+\hat{j}-3\hat{k}$ and $3\hat{i}+\hat{j}-\hat{k}$ which displace it from a point $\hat{i}+2\hat{j}+3\hat{k}$ to the point $5\hat{i}+4\hat{j}+\hat{k}$. The work done in standard units by the forces is given by

If $\overline{\mathrm{a}},\overline{\mathrm{b}},\overline{\mathrm{c}}$ are non-coplanar vectors and $\lambda$ is a real number, then the vectors $\overline{\mathrm{a}}+2\overline{\mathrm{b}}+3\overline{\mathrm{c}},\lambda \overline{\mathrm{b}}+4\overline{\mathrm{c}}$ and …

Let $\overline{\mathrm{u}},\overline{\mathrm{v}},\overline{\mathrm{w}}$ be such that $|\overline{\mathrm{u}}|=1,|\overline{\mathrm{v}}|=2,|\overline{\mathrm{w}}|=3$. If the projection $\overline{\mathrm{v}}$ along $\overline{\mathrm{u}}$ is equal to that of …

Let $\overline{\mathrm{a}},\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be non-zero vectors such that $(\overline{\mathrm{a}}\times \overline{\mathrm{b}})\times \overline{\mathrm{c}}=\frac{1}{3}|\overline{\mathrm{b}}||\overline{\mathrm{c}}|\overline{\mathrm{a}}$. If …

With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N . If they act at right angles, then their resultant is 3 N . Then the forces are

A velocity $\frac{1}{4}\mathrm{m}/\mathrm{s}$ is resolved into two components along OA and OB making angles $30^{\circ }$ and $45^{\circ }$ respectively with the given velocity. Then the component along OB is