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  • Please solve RD Sharma Class 12 Chapter 26 Directions Cosines and Direction Ratio Exercise Multiple Choice Question, question 6 Maths textbook solution.

Please solve RD Sharma Class 12 Chapter 26 Directions Cosines and Direction Ratio Exercise Multiple Choice Question, question 6 Maths textbook solution.

Answers (1)

Answer: (c) -1

Hint: Use section formula

Given: x-coordinate of point P(x,y,z) on the join of Q(2,2,1) and R(5,1,-2) is 4

To Find: z-coordinate of point P(x,y,z)

Solution:

Suppose point P divide the line segment joining the points Q(2,2,1) and R(5,1,-2) in ratio t:1

Using section formula, coordinates of point P

(x, y, z)=\left[\frac{t(5)+2}{t+1}, \frac{t(1)+2}{t+1}, \frac{t(-2)+1}{t+1}\right]

x-coordinate of point P is 4

\begin{aligned} &\Rightarrow \frac{5 t+2}{t+1}=4 \\ &\Rightarrow 5 t+2=4(t+1) \\ &\Rightarrow t=2 \end{aligned}

Now z-coordinate will be

\begin{aligned} &z=\frac{t(-2)+1}{t+1} \\ &z=\frac{2(-2)+1}{t+1} \\ &z=\frac{-4+1}{2+1} \\ &z=\frac{-3}{3} \\ &z=-1 \end{aligned}

Therefore z coordinate of P is -1. Hence option (c) -1 is correct.

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