First slide

Scalars and Vectors

Question

When $\vec{A} \cdot \vec{B} = - | A | | B |$ then

Moderate

A

$\vec{A}$ and $\vec{B}$ are perpendicular to each other
B

$\vec{A}$ and $\vec{B}$ act in the same direction
C

$\vec{A}$ and $\vec{B}$ act in the opposite direction
D

$\vec{A}$ and $\vec{B}$ can act in any direction

Solution

$\begin{array}{l} \vec{A} \cdot \vec{B} = A B \cos θ \\ In the problem \vec{A} \cdot \vec{B} = - A B, i.e., \cos θ = - 1 ∴ θ = 180^{\circ} \\ i.e. \vec{A} and \vec{B} acts in the opposite direction. \end{array}$

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