Question

Find the equation of the line that passes through the point (2,3,4) and is perpendicular to the plane 2x-y + 3z = 4

a. x=4+2t , y=2-t, z=7-3t

b. x=2+2t , y=3-t, z=4+t

c. x=2-2t , y=-3+t, z=4-3t

d. x=-2+4t , y=5-2t, z=-2+6t

e. another solution

Answer 1

we are given plane as

2x-y + 3z = 4

and it is passing through (2,3,4)

now, we can get equation of line

(2, y, z) = (2, 3, 4) + t2, -1,3)

$(x,y,z)=(2+2t,3-t,4+3t)$

so, we get

$x=2+2t,y=3-t,z=4+3t$............Answer