Collinearity of points MCQ Quiz in मराठी - Objective Question with Answer for Collinearity of points - मोफत PDF डाउनलोड करा
Last updated on Apr 1, 2025
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.
Answer (Detailed Solution Below)
Collinearity of points Question 1 Detailed Solution
CONCEPT:
If the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) be collinear then
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.
Answer (Detailed Solution Below)
Collinearity of points Question 2 Detailed Solution
CONCEPT:
If the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) be collinear then
Collinearity of points Question 3:
The points (-5, 1), (1, k) and (4, -2) are collinear if the value of k is
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
Collinearity of points Question 4 Detailed Solution
Again,
Since, P, Q and R are co-linear points, hence
On Solving, we get:-
Hence, answer is option-(D).