Question 10 The equation of the line in vector form passing through the point (โ1, 3, 5) and parallel to line (๐ฅ โ 3)/2 = (๐ฆ โ 4)/3, z = 2. is (a) ๐ โ = (โ๐ ฬ + 3๐ ฬ + 5๐ ฬ) + ๐ (2๐ ฬ + 3๐ ฬ + ๐ ฬ) (b) ๐ โ = (โ๐ ฬ + 3๐ ฬ + 5๐ ฬ) + ๐ (2๐ ฬ + 3๐ ฬ) (c) ๐ โ = (2๐ ฬ + 3๐ ฬ โ 2๐ ฬ) + ๐ (โ๐ ฬ + 3๐ ฬ + 5๐ ฬ) (d) ๐ โ = (2๐ ฬ + 3๐ ฬ) + ๐ (โ๐ ฬ + 3๐ ฬ + 5๐ ฬ)
Equation of a line passing through a point with position vector ๐ โ and parallel to vector ๐ โ is
๐ โ = ๐ โ + ๐๐ โ
Here,
Point is (โ1, 3, 5)
So, ๐ โ = โ๐ ฬ + 3๐ ฬ + 5๐ ฬ
And it is parallel to line
(๐ฅ โ 3)/2 = (๐ฆ โ 4)/3, z = 2
This means that z-component of equation is 0
So, line is (๐ฅ โ 3)/2 = (๐ฆ โ 4)/3 = (๐ง โ 2)/0
So, ๐ โ = 2๐ ฬ + 3๐ ฬ + 0๐ ฬ = 2๐ ฬ + 3๐ ฬ
Thus, Equation of line is
๐ โ = (โ๐ ฬ + 3๐ ฬ + 5๐ ฬ) + ๐ (2๐ ฬ + 3๐ ฬ)
So, (b) is the correct answer

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.