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

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

Answers (1)

Answer:

90^{\circ}

Hint:

\cos \theta=\frac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \cdot \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}

Given:

Distance ratio are proportional to (1, -2, 1) and(4, 3, 2).

Solution:

Here, a_1, b_1, c_1= 1, -2, 1 
a_2, b_2, c_2= 4, 3, 2

We know that,

\begin{aligned} &\cos \theta=\frac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \cdot \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}} \\ &\therefore a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2} \\ &=(1)(4)+(-2)(3)+(1)(2) \\ &=4-6+2 \\ &=0 \\ &\cos \theta=0 \\ &\theta=90^{\circ} \end{aligned}

 

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