Collinearity of points MCQ Quiz in தமிழ் - Objective Question with Answer for Collinearity of points - இலவச PDF ஐப் பதிவிறக்கவும்

Last updated on Apr 13, 2025

பெறு Collinearity of points பதில்கள் மற்றும் விரிவான தீர்வுகளுடன் கூடிய பல தேர்வு கேள்விகள் (MCQ வினாடிவினா). இவற்றை இலவசமாகப் பதிவிறக்கவும் Collinearity of points MCQ வினாடி வினா Pdf மற்றும் வங்கி, SSC, ரயில்வே, UPSC, மாநில PSC போன்ற உங்களின் வரவிருக்கும் தேர்வுகளுக்குத் தயாராகுங்கள்.

Latest Collinearity of points MCQ Objective Questions

Top Collinearity of points MCQ Objective Questions

Collinearity of points Question 1:

If the points (2, - 1, 2), (1, 2, - 3) and (3, k, 7) are collinear, then find the value of k.

  1. 3
  2. - 3
  3. 4
  4. - 4

Answer (Detailed Solution Below)

Option 4 : - 4

Collinearity of points Question 1 Detailed Solution

CONCEPT:

If the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) be collinear then |x1y1z1x2y2z2x3y3z3|=0

CALCULATION:
 
Given: The points (2, - 1, 2), (1, 2, - 3) and (3, k, 7) are collinear
As we know that, if the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) be collinear then |x1y1z1x2y2z2x3y3z3|=0
Here, x1 = 2, y1 = - 1, z1 = 2, x2 = 1, y2 = 2, z2 = - 3, x3 = 3, y3 = k and z3 = 7
 
⇒ |2121233k7|=0
 
⇒ 2 × (14 + 3k) + 1 × (7 + 9) + 2 × (k - 6) = 0
 
⇒ 28 + 6k + 16 + 2k - 12 = 0
 
⇒ 32 + 8k = 0
 
⇒k = - 4
 
Hence, option D is the correct answer.

Collinearity of points Question 2:

If the points (1, 3, 1), (2, - 1, k) and (0, 7, 3) are collinear, then find the value of k.

  1. 0
  2. 1
  3. - 1
  4. None of these

Answer (Detailed Solution Below)

Option 3 : - 1

Collinearity of points Question 2 Detailed Solution

CONCEPT:

If the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) be collinear then |x1y1z1x2y2z2x3y3z3|=0

CALCULATION:
 
Given: The points (1, 3, 1), (2, - 1, k) and (0, 7, 3) are collinear
As we know that, if the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) be collinear then |x1y1z1x2y2z2x3y3z3|=0
Here, x1 = 1, y1 = 3, z1 = k, x2 = 2, y2 = - 1, z2 = k, x3 = 0, y3 = 7 and z3 = 3
 
⇒ |13121k073|=0
 
⇒ 1 × (- 3 - 7k) - 3 × (6 - 0) + 1 × (14 - 0) = 0
 
⇒ - 3 - 7k - 18 + 14 = 0
 
⇒ k = - 1
 
Hence, option C is the correct answer.

Collinearity of points Question 3:

The points (-5, 1), (1, k) and (4, -2) are collinear if the value of k is

  1. -1
  2. 2
  3. 3
  4. 1

Answer (Detailed Solution Below)

Option 1 : -1

Collinearity of points Question 3 Detailed Solution

Given:

Points: (-5, 1), (1, k), and (4, -2)

Formula used:

For three points to be collinear, the area of the triangle formed by them must be zero.

Area of a triangle using coordinates:

Area = (1/2) × [x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Calculation:

Since the points are collinear:

(1/2) × [-5(k + 2) + 1(-2 - 1) + 4(1 - k)] = 0

-5(k + 2) + 1(-3) + 4(1 - k) = 0

-5k - 10 - 3 + 4 - 4k = 0

-9k - 9 = 0

-9k = 9

k = -1

∴ The value of k is -1.

Collinearity of points Question 4:

If points P(4,5,x),Q(3,y,4) and R(5,8,0) are colinear, then the value of x+y is

  1. 4
  2. 3
  3. 5
  4. 4

Answer (Detailed Solution Below)

Option 4 : 4

Collinearity of points Question 4 Detailed Solution

PR=(54)i^+(85)j^+(0x)k^

PR=i^+3j^xk^

Again, QR=(53)i^+(8y)j^+(04)k^

QR=2i^+(8y)j^4k^

Since, P, Q and R are co-linear points, hence

12=38y=x4

On Solving, we get:-

x=2,y=2

x+y=4

Hence, answer is option-(D).

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