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Q.

If $O P = 8$ and $\vec{O P}$ makes angles $45 °$ and $60 °$ with $O X -$ axis and $O Y$ - axis respectively, then $\vec{O P} = ?$

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a

$\frac{1}{4} (\sqrt{2} i + j \pm k)$

b

$8 (\sqrt{2} i + j \pm k)$

c

$4 (\sqrt{2} i + j \pm k)$

d

$\frac{1}{8} (\sqrt{2} i + j \pm k)$

answer is B.

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Detailed Solution

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Here is the only vector $4 (\sqrt{2} i + j \pm k),$ whose length is 8.

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If OP=8 and OP→ makes angles 45° and 60° with OX- axis and OY- axis respectively, then OP→=?