JEE Main201815 Apr 2018Morning ShiftMathematicsVector AlgebraActual

If a , b , and c are unit vectors such that a +2 b +2 c = 0 , then | a c | is equal to

Options

A1 4
B15 4
C15 16
D15 16

Correct answer

B. 15 4

Step-by-step solution

aligned & a +2 b +2 c = 0 [Given] & a +2 c =-2 b &( a +2 c ) ( a +2 c )=(-2 b )(-2 b ) a a +4 c c +4 a c =4 b b & 1+4+4 a c =4 & a c = -1 4 &| a c |^2+| a c |^2=1( a is unit vector ) & 1 16 +| a c |^2=1 &| a c |^2= 15 16 &| a c |^2= 15 4 aligned

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