If a and b are unit vectors, then the vector defined as V=(a+b)×(a+b) is collinear to the vector

V=(a×b)×a+(a×b)×b =b-(a·b)a+(a·b)b-a =(b-a)+(b-a)(a·b)V=(b-a)(1+a·b)=λ(b-a)

If a and b are unit vectors, then the vector defined as V=(a+b)×(a+b) is collinear to the vector

V=(a×b)×a+(a×b)×b =b-(a·b)a+(a·b)b-a =(b-a)+(b-a)(a·b)V=(b-a)(1+a·b)=λ(b-a)

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If $a$ and $b$ are unit vectors, then the vector defined as $V = (a + b) \times (a + b)$ is collinear to the vector

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$a + b$

$a + 2 b$

$b - a$

$2 a - b$

answer is B.

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Detailed Solution

$\begin{array}{rcl} V & = & (a \times b) \times a + (a \times b) \times b \\ = & b - (a \cdot b) a + (a \cdot b) b - a \\ = & (b - a) + (b - a) (a \cdot b) \\ V & = & (b - a) (1 + a \cdot b) = λ (b - a) \end{array}$

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