Question

Find a value of $\alpha$ such that velocities $\overrightarrow{v_A}=3\hat{i}+6\hat{j}and\overrightarrow{v_B}=2\hat{i}+\alpha \hat{j}$ represent velocities of cars moving in the same direction.

• A. $\alpha =2$
• B. $\alpha =4$
• C. $\alpha =3$
• D. $\alpha =1$

Answer 1

The correct option is B $\alpha =4$

$\overrightarrow{V_A}=\lambda \overrightarrow{V_B}\Rightarrow 3\hat{i}+6\hat{j}=\lambda (2\hat{i}+\alpha \hat{j})$
$3=2\lambda$
$6=\alpha \lambda$
$\frac{3}{6}=\frac{2}{\alpha }$
$\alpha =4$