What is the angle between resultant of A + B and A × B. (a) π rad (b) 0° (c) π/4 rad (d) π/2 rad

Answer: (d). A × B is perpendicular to the plane containing A and B. A + B lies in that plane, so (A + B) · (A × B) = 0. So the angle is (d) π/2 rad.

What is the angle between resultant of A + B and A × B. | MHT CET 2020 (19 Oct, Shift 2)

Q14MHT CET 2020 · 19 OCT · SHIFT 2Easy

Vector (Cross) Product

What is the angle between resultant of $A + B$ and $\mathbf{A} \times \mathbf{B}$ .

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Answer: (d)

$\mathbf{A} \times \mathbf{B}$ is perpendicular to the plane containing $\mathbf{A}$ and $\mathbf{B}$ .
$\mathbf{A} + \mathbf{B}$ lies in that plane, so $(\mathbf{A} + \mathbf{B}) \cdot (\mathbf{A} \times \mathbf{B}) = 0$ .
So the angle is (d) $\frac{\pi}{2}$ rad.