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  • Need solution for RD Sharma Maths Class 12 Chapter 26 Directions Cosines and Direction Ratios Exercise Very Short Answer Question, question 6.

Need solution for RD Sharma Maths Class 12 Chapter 26 Directions Cosines and Direction Ratios Exercise Very Short Answer Question, question 6.

Answers (1)

Answer:

13 units

Hint:

d=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}+\left(z_{1}-z_{2}\right)^{2}}

Given:

P(3, -5, 12 )

Solution:

The direction cosines of x-axis is b_1 (1, 0, 0)

Let A(\lambda, 0,0) be the point on x-axis.

From P(3, -5, 12 ) drawn a line on x-axis perpendicularly in x-axis at A(\lambda, 0,0).

Distance of cosines of AP=b_2\left ( 3-\lambda ,-5, 12 \right )

we know that 

\begin{aligned} &\overrightarrow{b_{1}} \cdot \overrightarrow{b_{2}}=0 \\ &\Rightarrow 1 \times(3-\lambda)=0 \\ &\Rightarrow 3-\lambda=0 \\ &\Rightarrow \lambda=3 \\ &\therefore A=(3,0,0) \\ &A P=\sqrt{(3-3)^{2}+(0+5)^{2}+(12-0)^{2}} \\ &=\sqrt{25+144} \\ &=\sqrt{169} \\ &=13 \end{aligned}

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