Question

Write the vector equation if the line passing through (1,2,3) and perpendicular to plane r.(1+2j-5k)+9=0

Answer 1

Hope will help you if any more doubt ask in comments

Answer 2

Given:

A line passing through (1,2,3) and perpendicular to plane r.(1+2j-5k)+9=0.

To Find:

Write the vector equation of the line.

Solution:

Since the line is perpendicular to the plane , vector parallel to the line will be the normal vector of the plane.

Also the line passes through ( 1, 2, 3) .

Therefore line equation is :

• $\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{-5}$
• Parameter = t
• x - 1 = t  = > x = t + 1
• y - 2 = 2t = > y = 2 + 2t
• z - 3 = -5t = > z = 3 - 5t

Therefore vector equation of the line is, i + 2j + 3k + t ( 1 + 2j - 5k)