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Question

Find the direction cosines of a line which is perpendicular to the lines whose direction ratios are (1,1,2) and (2,1,1).

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Solution

let

a=ij+2k and b=2i+jk

a×b=∣ ∣ijk112211∣ ∣

a×b=i+5j+3k

|a×b|=(1)2+52+32=35

Direction cosines are :(±135,±535,±335)

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