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Question

Check whether the two vectors, A=3ˆi7ˆj+9ˆkandB=2ˆi21ˆj+6ˆkare parallel to each other

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Solution

If2vectorsareparalleltoeachother,
cosθ=1
¯¯¯a.¯¯b=¯¯¯a.¯¯b
¯¯¯a.¯¯b=(3i7j+9k).(2i21j+6k)
6+147+54=207=L.H.S
¯¯¯¯A=9+49+81=139
¯¯¯¯B=4+441+36=481
¯¯¯¯A.¯¯¯¯B=139×481=R.H.S
L.H.SR.H.S
Theyarenotparallel.

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