Question

The ratio in which 2i+3j-7k divides the join of i+j+k and 5i+9j-31k

Answer 1

Given: Two points of line joining are i+j+k and 5i + 9j - 31k.

To find: The ratio in which 2i + 3j - 7k divides the join of two points.

Solution:

• Very first lets write the points, those are:

            i+j+k = (1,1,1)

            5i+9j-31k = (5,9,-31)

            2i+3j-7k = (2,3,-7)

• Now by ratio formula, we have

            mx2 + nx1 / m + n,     my2 + ny1 / m + n

• Let the ratio be m:1.

• So putting the values in the formula we get:

            mx2+nx1/m+n = m(5) + 1 / m + 1 = 2

                                    = 5m + 1 = 2m + 2

                                       3m = 1

                                       m = 1/3

• So the ratio is 1/3 : 1 = 1 : 3

Answer:

The ratio in which 2i+3j-7k divides the join of i+j+k and 5i+9j-31k is 1:3