Question

If a vector $\hat{i}+x\hat{j}$ is rotated through an angle $\theta$ and its magnitude is doubled, then it becomes $\hat{i}+4x\hat{j}$. The value of $x$ may be

• A. $-\frac{2}{3}$
• B. $\frac{1}{2}$
• C. $\frac{2}{3}$
• D. $2$

Answer 1

The correct option is B $\frac{1}{2}$

Since there is only one unknown $x$, we use one information that the magnitude of vector $\hat{i}+4x\hat{j}$ is double of vector $\hat{i}+x\hat{j}.$

$2\times \sqrt{1^2+x^2}=\sqrt{1^2+4(x{)}^2}$
Taking square on both sides we get,
$4(1+x^2)=(1+16x^2)$
$(4+4x^2)=(1+16x^2)$
$12x^2=3$
$x=\pm \frac{1}{2}$