Ncert Exercises & Solutions

The angle between

A =^i +^j

$\mathrm{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}$ and

B =^i -^j

$\mathrm{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$ is:
1.

45^{\circ}

$45^{\circ}$
2.

90^{\circ}

$90^{\circ}$
3.

- 45^{\circ}

$-45^{\circ}$
4.

180^{\circ}

$180^{\circ}$

(b) Hint: Use the dot product.

Step 1: Find the dot product.

Given,

We know that

$\begin{array}{l} A \cdot B = | A ∥ B | \cos θ \\ \Rightarrow (\hat{i} + \hat{j}) \cdot (\hat{i} - \hat{j}) = (\sqrt{1 + 1}) (\sqrt{1 + 1}) \cos θ \end{array}$

Step 2: Find the angle between the vectors.
where

$θ$ is the angle between A and B

$\begin{array}{l} \Rightarrow \cos θ = \frac{1 - 0 + 0 - 1}{\sqrt{2} \sqrt{2}} = \frac{0}{2} = 0 \\ \Rightarrow θ = 90^{\circ} \end{array}$

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