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  • Provide solution for RD Sharma Maths Class 12 Chapter 26 Directions Cosines and Direction Ratios Exercise Multiple Choice Question, question 15.

Provide solution for RD Sharma Maths Class 12 Chapter 26 Directions Cosines and Direction Ratios Exercise Multiple Choice Question, question 15.

Answers (1)

Final Answer: (a) 2

Hint: Use section formula

Given: Points (3,2,-1) and (6,2,-2) and P(5,y,z)

To Find: y-coordinate of P(5,y,z)

Solution: Let P divide the line joining (3,2,-1)and (6,2,-2) in t:1

Using section formula

\begin{aligned} &(5, y, z)=\left[\frac{t(6)+3}{t+1}, \frac{t(2)+2}{t+1}, \frac{t(-2)+(-1)}{t+1}\right] \\ &(5, y, z)=\left[\frac{6 t+3}{t+1}, \frac{2 t+2}{t+1}, \frac{-2 t-1)}{t+1}\right] \end{aligned}

Comparing x-coordinate

\begin{aligned} &5=\frac{6 t+3}{t+1} \\ &5(t+1)=6 t+3 \\ &t=2 \end{aligned}

Now comparing y-coordinate

\begin{aligned} &y=\frac{2 t+2}{t+1} \\ &y=\frac{2(2)+2}{2+1} \\ &y=2 \end{aligned}

Therefore, y-coordinate of P(5,y,z) is 2. hence option(a) is correct.

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