Q. 25

# Find the image of the point (5, 9, 3) in the line Given: Equation of line is To find: image of point (5, 9, 3)

Formula Used: Equation of a line is

Vector form: Cartesian form: where is a point on the line and with b1 : b2 : b3 being the direction ratios of the line.

If 2 lines of direction ratios a1:a2:a3 and b1:b2:b3 are perpendicular, then a1b1+a2b2+a3b3 = 0

Mid-point of line segment joining (x1, y1, z1) and (x2, y2, z2) is Explanation:

Let So the foot of the perpendicular is (2λ + 1, 3λ + 2, 4λ + 3)

The direction ratios of the perpendicular is

(2λ + 1 - 5) : (3λ + 2 - 9) : (4λ + 3 - 3)

(2λ – 4) : (3λ – 7) : (4λ)

Direction ratio of the line is 2 : 3 : 4 From the direction ratio of the line and the direction ratio of its perpendicular, we have

2(2λ – 4) + 3(3λ – 7) + 4(4λ) = 0

4λ – 8 + 9λ – 21 + 16λ = 0

29λ = 29

λ = 1

So, the foot of the perpendicular is (3, 5, 7)

The foot of the perpendicular is the mid-point of the line joining (5, 9, 3) and (α, β, γ)

So, we have   So, the image is (1, 1, 11)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Revision of straight lines important formulas in one shot59 mins  Concept Builder Questions of straight Lines (Quiz Session)55 mins  Magnetic field due to current carrying straight wire37 mins  Translation Process37 mins  Interactive Quiz on Bacterial Diseases29 mins  Immune System Disorders60 mins  Interactive Quiz on Cancer36 mins  Human health & diseases (Drug)56 mins  Get to know all about Immune System60 mins  Interactive Quiz on Magnetic field due to straight wire & circular loop41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 