First slide

Scalars and Vectors

Question

Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneously ${\vec{F}}_{1} = - 4 \hat{i} - 5 \hat{j} + 5 \hat{k}, {\vec{F}}_{2} = 5 \hat{i} + 8 \hat{j} + 6 \hat{k}$ , ${\vec{F}}_{3} = - 3 \hat{i} + 4 \hat{j} - 7 \hat{k} and {\vec{F}}_{4} = 2 \hat{i} - 3 \hat{j} - 2 \hat{k}$ then the particle will move

Easy

A

In x-y plane
B

In y-z plane
C

ln x-z plane
D

Along x-axis

Solution

$\begin{array}{l} F_{1} + {\vec{F}}_{2} + {\vec{F}}_{3} + {\vec{F}}_{4} \\ = (- 4 \hat{i} + 5 \hat{i} - 3 \hat{i} + 2 \hat{i}) + (- 5 \hat{j} + 8 \hat{j} + 4 \hat{j} - 3 \hat{j}) \\ + (5 \hat{k} + 6 \hat{k} - 7 \hat{k} - 2 \hat{k}) = 4 \hat{j} + 2 \hat{k} \\ ∴ The particle will move in y - z plane. \end{array}$

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