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  • Explain solution RD Sharma Class 12 Chapter 26 Direction Cosines and Direction Ratios Exercise Very Short Answer Question, question 19 Maths.

Explain solution RD Sharma Class 12 Chapter 26 Direction Cosines and Direction Ratios Exercise Very Short Answer Question, question 19 Maths.

Answers (1)

Answer:

\frac{\pi}{3}

Hint:

\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1

Given:

a makes angle \frac{\pi}{3} with i,\frac{\pi}{4} with j and \theta with k

Solution:

Angle of a with i=\frac{\pi}{3}

\begin{aligned} &\Rightarrow(x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot(1 \hat{\imath}+0 \hat{\jmath}+0 \hat{k})=1 \times 1 \times \frac{1}{2}, \; \; \; \; \; \; \; \; \; \; \quad \text { since }|a|=1 \\ &\Rightarrow x \times 1=\frac{1}{2} \\ &\Rightarrow x=\frac{1}{2} \end{aligned}

Similarly,

\gamma =\frac{1}{\sqrt{2}}

let \gamma be the angle.

\begin{aligned} &\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\ &\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{\sqrt{2}}\right)^{2}+\cos ^{2} \gamma=1 \\ &\cos ^{2} \gamma=\frac{1}{4} \\ &\Rightarrow \cos \gamma=\pm \frac{1}{2} \\ &\gamma=\frac{\pi}{3} \end{aligned}

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