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  • Please solve RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 25 maths textbook solution

Please solve RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 25 maths textbook solution

Answers (1)

Answer:
Option (d) \frac{\pi}{3}

Vector a and b are perpendicular if their dot product is zero.

Given:

\theta is an acute angle

\sin \hat{\theta} \hat{i}+\cos \theta \hat{j} \text { and } \hat{i}-\sqrt{3} \hat{j}  are perpendicular

(\sin \theta \hat{i}+\cos \theta \hat{j}) \cdot(\hat{i}-\sqrt{3} \hat{j})=0

Both are perpendicular to each other

\begin{aligned} &\sin \theta-\sqrt{3} \cos \theta=0 \\\\ &\sin \theta=\sqrt{3} \cos \theta \end{aligned}

\begin{aligned} &\frac{\sin \theta}{\cos \theta}=\sqrt{3} \\\\ &\tan \theta=\sqrt{3} \end{aligned}                            \begin{aligned} &{\left[\because \frac{\sin \theta}{\cos \theta}=\tan \theta\right]} \\ &{\left[\because \tan \frac{\pi}{3}=\sqrt{3}\right]} \end{aligned}

\theta=\frac{\pi}{3}

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