Question

Find a vector r⃗  of magnitude 3√2 units which makes an angle of π/4 π/2 with y and z-axes, respectively.​

Answer 1

Solution :-

From the give,

• m = cos π/4 = 1/√2

• n = cos π/2 = 0

Therefore, l² + m² + n² = 1

$\implies$ l² + (½) + 0 = 1

$\implies$ l² = 1 – ½

$\implies$ l = ±1/√2

Hence, the required vector is:

$\implies$ $\: \vec{r} \: = 3 \sqrt{2} \: (l \hat{i} \: + m \hat{j} + n \hat{k})$

$\implies$ $\vec{r} = 3 \sqrt{2} (± \frac{1}{ \sqrt{2} } \hat{i} \: + \: \frac{1}{ \sqrt{2}} \hat{j} + 0 \hat{k})$

$\huge {\boxed{ \red{\vec{r} \: = ±3 \hat{i} \: + 3 \hat{j}}}}$