If the vector $\overrightarrow b = 3\widehat j + 4\widehat k$ is written as the sum of a vector $\overrightarrow {{b_1}} ,$ paralel to $\overrightarrow a = \widehat i + \widehat j$ and a vector $\overrightarrow {{b_2}} ,$ perpendicular to $\overrightarrow a ,$ then $\overrightarrow {{b_1}} \times \overrightarrow {{b_2}} $ is equal to :

Question

$ - 3\widehat i + 3\widehat j - 9\widehat k$

$6\widehat i - 6\widehat j + {9 \over 2}\widehat k$

$ - 6\widehat i + 6\widehat j - {9 \over 2}\widehat k$

$3\widehat i - 3\widehat j + 9\widehat k$

Solution

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