JEE Advanced2010MathematicsVector AlgebraActual

If a and b are vectors in space given by a = i -2 j 5 and b = 2 i + j +3 k 14 , then the value of (2 a + b ) [( a b ) ( a -2 b )] is

Correct answer

Step-by-step solution

From the given information, it is clear that gathered a = i -2 j 5 | a |=1,| b |=1, a b =0 Now, (2 a + b ) [( a b ) ( a -2 b )] gathered aligned & =(2 a + b ) [a^2 b -( a b ) a +2 b^2 a . & =[2 a + b ] [ b +2 a ]=4 a ^2+ b ^2 & =4 1+1=5 [as a b=0] aligned

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