JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q84

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MathematicsSingle correct+4 / -1Question 84 of 90

If the vector $\vec b=3\hat j+4\hat k$ is written as the sum of a vector $\vec b_1$ , parallel to $\vec a=\hat i+\hat j$ and a vector $\vec b_2$ , perpendicular to $\vec a$ , then $\vec b_1\times\vec b_2$ is equal to :

-3\hat i+3\hat j-9\hat k

6\hat i-6\hat j+\dfrac92\hat k

-6\hat i+6\hat j-\dfrac92\hat k

3\hat i-3\hat j+9\hat k

Answer and worked solution

Official answer: B

$\vec b_1=\dfrac{\vec b\cdot\vec a}{|\vec a|^2}\vec a=\frac32(\hat i+\hat j)$ and $\vec b_2=\vec b-\vec b_1=-\frac32\hat i+\frac32\hat j+4\hat k$ . Then
$\vec b_1\times\vec b_2=\frac32(4\hat i-4\hat j+3\hat k)=6\hat i-6\hat j+\frac92\hat k.$

Topics:Cross product Dot product

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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 84