Question

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

Answer 1

Given:

Two vectors A = -2i+3j+5k and  B = 7i-k  and a point P =  i+2j+3k.

To Find:

The ratio in which i+2j+3k divides the join -2i+3j+5k and 7i-k .

Solution:

Let x be the ratio in which the point P divides the line segment joining A and B.

• Then :
• (A + xB )/ ( 1+x) = P
• (-2i + 3j + 5k) + (7xi - xk ) = (1+x)i + (2+2x)j + (3+3x)k
• (7x-2)i + 3j + (5-x)k = (1+x)i + (2+2x)j + (3+3x)k

Comparing coefficients ,

• 7x - 2 = 1 + x
• 6x = 3
• x = 1/2
• A gets twice and B is same.
• 2A + B = 3P

This comes same if we compare any terms.

• Therefore ratio : 2:1

The ratio in which i+2j+3k divides the join -2i+3j+5k and 7i-k is 2:1.