Question

A vector \(\overset{̄}{r}\) of magnitude \(3\sqrt{2}\) units which makes angles of \(\frac{π}{4}\) and \(\frac{π}{2}\) respectively with Y and Z axes is

• A. \(\overset{̄}{r} = \pm 3\hat{i}+3\hat{j}\)
• B. \(\overset{̄}{r} = \hat{i}+\hat{j}\)
• C. \(\overset{̄}{r} = \pm 2\hat{i}+3\hat{j}\)
• D. \(\overset{̄}{r} = \pm 5\hat{i}+\hat{j}\)

Hint:

Use direction cosines: l squared plus m squared plus n squared equals 1, then multiply by the magnitude.

Answer 1

The Correct Option is A

Step 1: Use components.
The component along $Y$ is $|\bar{r}|\cos\dfrac{\pi}{4} = 3\sqrt{2}\cdot\dfrac{1}{\sqrt{2}} = 3$.

Step 2: Z component.
Making an angle of $\pi/2$ with the Z axis means the Z component is 0.

Step 3: X component.
The magnitude gives $x^2 + 9 = 18$, so $x = \pm 3$.

Final Answer:
Option (A). \[ \boxed{\bar{r} = \pm 3\hat{i} + 3\hat{j}} \]