The ratio in which {i}+2{j}+3{k} divides the join of -2{i}+3{j}+5{k} and 7{i}-{k} is

Correct Answer is : 2:12 : 12:1

Correct Answer is : 2:12 : 12:1

Test Index

EAMCET Engineering 2007 Solved Paper

Section: Mathematics

Question : 116 of 160

Marks: +1, -0

The ratio in which

\hat{i}+2\hat{j}+3\hat{k}

-2\hat{i}+3\hat{j}+5\hat{k}

7\hat{i}-\hat{k}

Solution:

Let the line joining the points with position vectors

-2\hat{i}+3\hat{j}+5\hat{k}

and

7\hat{i}-\hat{k}

be divide in the ratio

\lambda : 1

\hat{i}+2\hat{j}+3\hat{k}

\therefore \; \frac{\hat{\lambda (7\hat{i}-\hat{k})+(-2\hat{i}+3\hat{j}+5\hat{k})}}{\lambda+1}=\hat{i}+2\hat{j}+3\hat{k}

\Rightarrow \;\; (7\lambda-2)\hat{i}+3\hat{j}+(5-\lambda)\hat{k}=(\lambda+1)\hat{i}

+2(\lambda+1)\hat{j}+3(\lambda+1)\hat{k}

On equating the coefficient of

\hat{i}

, we get

\;7\lambda-2\;=\lambda+1

\;\lambda\;=2

Hence, ratio

\lambda : 1 = 2 : 1

Go to Question:

Prev Question

Next Question