Question 10 The equation of the line in vector form passing through the point (β1, 3, 5) and parallel to line (π₯ β 3)/2 = (π¦ β 4)/3, z = 2. is (a) π β = (βπ Μ + 3π Μ + 5π Μ) + π (2π Μ + 3π Μ + π Μ) (b) π β = (βπ Μ + 3π Μ + 5π Μ) + π (2π Μ + 3π Μ) (c) π β = (2π Μ + 3π Μ β 2π Μ) + π (βπ Μ + 3π Μ + 5π Μ) (d) π β = (2π Μ + 3π Μ) + π (βπ Μ + 3π Μ + 5π Μ)
Equation of a line passing through a point with position vector π β and parallel to vector π β is
π β = π β + ππ β
Here,
Point is (β1, 3, 5)
So, π β = βπ Μ + 3π Μ + 5π Μ
And it is parallel to line
(π₯ β 3)/2 = (π¦ β 4)/3, z = 2
This means that z-component of equation is 0
So, line is (π₯ β 3)/2 = (π¦ β 4)/3 = (π§ β 2)/0
So, π β = 2π Μ + 3π Μ + 0π Μ = 2π Μ + 3π Μ
Thus, Equation of line is
π β = (βπ Μ + 3π Μ + 5π Μ) + π (2π Μ + 3π Μ)
So, (b) is the correct answer
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.