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Comprehensive Master Sheet: Vectors
Student Name: ____________________________________
Class: 11th (CBSE/NEET/JEE)
Subject: Physics
Section A: Vector Addition & Components
1.
Two vectors $\vec{A}$ and $\vec{B}$ of magnitude 6 units and 8 units act at an angle of $60^\circ$. Find magnitude of resultant vector $\vec{R}$.
2.
Find a unit vector parallel to the resultant of $\vec{A} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{B} = \hat{i} - 2\hat{j} + 4\hat{k}$.
Section B: Dot Product & Projections
3.
Find the angle between $\vec{A} = 3\hat{i} + 4\hat{j}$ and $\vec{B} = 4\hat{i} - 3\hat{j}$.
4.
Find the value of $m$ for which vectors $\vec{A} = 2\hat{i} + m\hat{j} + \hat{k}$ and $\vec{B} = 4\hat{i} - 2\hat{j} - 2\hat{k}$ are perpendicular.
Section C: Cross Product & Applications
5.
Find area of the parallelogram determined by vectors $\vec{A} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{B} = 2\hat{i} + \hat{j} - 4\hat{k}$.
6.
Calculate torque $\vec{\tau} = \vec{r} \times \vec{F}$ where $\vec{r} = 7\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{F} = -3\hat{i} + \hat{j} + 5\hat{k}$.
