First slide

Vectors

Question

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$ . If angle between $\vec{A}$ and $\vec{B}$ is $θ$ , then what is the angle between resultant and $\vec{B}$

Moderate

A

$\frac{B sinθ}{B + A cosθ}$
B

$\frac{A sinθ}{A + B cosθ}$
C

$\frac{A sinθ}{B + A cosθ}$
D

$\frac{B sinθ}{A + B cosθ}$

Solution

The angle between resultant $\vec{C}$ and $\vec{B}$ is
$tanβ = \frac{A sinθ}{B + A cosθ}$
where A and B are magnitudes of $\vec{A}$ and $\vec{B}$ .

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