Question

Find the coordinate of the point where the line x + 1/2= y +2/3= z +3/4 meets the plane x + y + 4z = 6

Answer 1

Answer:

(1, 1, 1)

Step-by-step explanation:

Given line is

$\frac{x+1}{2}=\frac{y+2}{3}=\frac{z+3}{4}=m(say)$

Any point on this line can be put in the form

(2m-1, 3m-2, 4m-3)

The required point lies on the plane

x + y + 4z = 6

we have

(2m-1)+(3m-2)+4(4m-3)=6

2m-1+3m-2+16m-12=6

21m=21

m=1

Therefore, the required point is

(2(1)-1, 3(1)-2, 4(1)-3)

(2-1, 3-2, 4-3)

(1, 1, 1)