If ` veca , vecb` are unit vectors such that the vector ` veca + 3vecb ` is peependicular to ` 7 veca - vecb and veca -4vecb` is prependicular to ` 7 veca -2vecb` then the angle between ` veca and vecb` isA. ` pi//6`B. ` pi//4`C. ` pi//3`D. ` pi//2`

If ` veca , vecb` are unit vectors such that the vector ` veca + 3vecb

1.	If ` veca , vecb` are unit vectors such that the vector ` veca + 3vecb ` is peependicular to ` 7 veca - vecb and veca -4vecb` is prependicular to ` 7 veca -2vecb` then the angle between ` veca and vecb` isA. ` pi//6`B. ` pi//4`C. ` pi//3`D. ` pi//2`
Answer» Correct Answer - C Let ` theta` be the angle between `veca and vecb` is we have, ` ( veca + 3vecb) bot ( 7 veca - 5vecb)` ` Rightarrow ( veca + 3vecb) . ( 7 veca -5vecb) =0 ` ` Rightarrow 7\|veca\|^(2) + 16(veca .vecb) -15 \|vecb\|^(2) =0` ` Rightarrow 15-30 cos theta =0 Rightarrow cos theta = 1/2 Rightarrow 1/2 Rightarrow theta = pi/3` And, ` (veca - 4 vecb ) bot ( 7veca - 2vecb)` ` Rightarrow (veca -4vecb) . ( 7 veca - 2 vecb) =0` ` Rightarrow 7\| veca\|^(2) + 8\|vecb\|^(2) -30 (veca .vecb) =0` ` Rightarrow 15-30 cos theta =0 Rightarrow = 1/2 Rightarrow = pi /3`

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