Ncert Exercises & Solutions

The angle between \(\mathrm{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(\mathrm{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) is:
1. \(45^{\circ} \)
2. \(90^{\circ} \)
3. \(-45^{\circ} \)
4. \(180^{\circ}\)

(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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