If a and b are two unit vectors then the vector a+b×a×b is parallel to

|a|=|b|=1(a+b)×(a×b)=a×(a×b)+b×(a×b) =(a·b)a-b+a-(a·b)b =(1+a·b) (a-b)

If a and b are two unit vectors then the vector a+b×a×b is parallel to

|a|=|b|=1(a+b)×(a×b)=a×(a×b)+b×(a×b) =(a·b)a-b+a-(a·b)b =(1+a·b) (a-b)

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If $a$ and $b$ are two unit vectors then the vector $(a + b) \times (a \times b)$ is parallel to

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$a - b$

$a + b$

$2 a - b$

$2 a + b$

answer is A.

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Detailed Solution

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

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