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  • Provide Solution for RD Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer Question 20

Provide Solution for RD Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer Question 20

Answers (1)

ANSWER:-  \theta = \frac{\pi}{3}

GIVEN:  \theta=\left(0, \frac{\pi}{3}\right) \text { and } \vec{a}=(\sin \theta \hat{i}+(\cos \theta \hat{j}) \text { and } \vec{b}=\hat{i}-\sqrt{3} \hat{j}+2 \hat{k}   are perpendicular

HINTS: use the formula of perpendicular vectors

SOLUTION:if vectors are perpendicular,then

\begin{aligned} &\Rightarrow[(\sin \theta \hat{i}+(\cos \theta) \hat{j}] \cdot[\hat{i}-\sqrt{3} \hat{j}+2 \hat{k}]=0 \\ & \end{aligned}

\Rightarrow \sin \theta-\sqrt{3} \cos \theta=0

Divide the equation by  \cos \theta

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

\Rightarrow \tan \theta-\sqrt{3}=0 \Rightarrow \tan \theta=\sqrt{3} \\

\Rightarrow \tan \theta-\tan \frac{\pi}{3} \Rightarrow \theta=\frac{\pi}{3}

 

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