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Question

# A vector →r is inclined at equal angles to OX,OY and OZ. If the magnitude of r is 6 units, then →r is equal to

A
3(ˆi+ˆj+ˆk)
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B
3(ˆi+ˆj+ˆk)
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C
23(ˆi+ˆj+ˆk)
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D
23(ˆi+ˆj+ˆk)
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Solution

## The correct options are C 2√3(ˆi+ˆj+ˆk) D −2√3(ˆi+ˆj+ˆk)Let r be inclined at an angle α to each axis, then l=m=n=cosαSince l2+m2+n2=1⇒3cos2α=1⇒cosα=±1√3If α is acute: l=m=n=1√3:|r|=6r=|r|(l^i+m^i+n^k)=6(1√3^i+1√3^j+1√3^k)=2√3(^i+^j+^k).If α is obtuse l=m=n=−1√3:|r|=6r=|r|(l^i+m^j+n^k)=6(−1√3^i+1√3^j+1√3^k)=−2√3(^i+^j+^k).

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