First slide

Vectors

Question

What is the angle between A = $5 (\hat{i} - \hat{j})$ and B = $5 (\hat{i} - \hat{j})$ ?

Moderate

A

90°
B

45°
C

0
D

60°

Solution

$\vec{A} \cdot \vec{B} = | \vec{A} | | \vec{B} | \cos θ$
Here
$\begin{array}{l} | \vec{A} | = \sqrt{[(5)^{2} + (5)^{2}]} = 5 \sqrt{2} \\ | \vec{B} | = \sqrt{(5)^{2} + (5)^{2}} = 5 \sqrt{2} \end{array}$
$∴ (5 \hat{i} - 5 \hat{j}) \cdot (5 \hat{i} - 5 \hat{j}) = 5 \sqrt{2} \times 5 \sqrt{2} \cos θ 5 \times 5 + 5 \times 5 = 25 \times 2 \cos θ$
$∴ \cos θ = 1 or θ = 0^{\circ}$

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