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Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
  • a)
    2 :1
  • b)
    3 :2
  • c)
    2 :4
  • d)
    2 : 3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Show that the points A(1, – 2, – 8), B (5, 0, – 2) a...


Therefore , AB and BC are parallel, but point B is common , so points , A,B,C are collinear. As 
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Show that the points A(1, – 2, – 8), B (5, 0, – 2) a...
To prove that the points A(1, 2, 8), B(5, 0, 2), and C(11, 3, 7) are collinear, we need to show that the vectors AB and BC are scalar multiples of each other. If AB and BC are scalar multiples, point B will divide AC in a specific ratio.

Step 1: Finding the vectors AB and BC
The vectors AB and BC can be found by subtracting the coordinates of the initial and final points.

Vector AB = B - A = (5, 0, 2) - (1, 2, 8) = (4, -2, -6)
Vector BC = C - B = (11, 3, 7) - (5, 0, 2) = (6, 3, 5)

Step 2: Checking if AB and BC are scalar multiples
To check if AB and BC are scalar multiples, we can take the ratio of their corresponding components.

Ratio of x-component: 4/6 = 2/3
Ratio of y-component: -2/3 = -2/3
Ratio of z-component: -6/5 = -6/5

Since the ratios are equal for all components, AB and BC are scalar multiples of each other.

Step 3: Finding the ratio in which B divides AC
To find the ratio in which B divides AC, we can use the ratio of the corresponding components of AB and BC.

Ratio of x-component: 2/3
Ratio of y-component: -2/3
Ratio of z-component: -6/5

Therefore, B divides AC in the ratio 2:3.

Hence, the correct answer is option 'D' (2:3).
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Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.a)2 :1b)3 :2c)2 :4d)2 : 3Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.a)2 :1b)3 :2c)2 :4d)2 : 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.a)2 :1b)3 :2c)2 :4d)2 : 3Correct answer is option 'D'. Can you explain this answer?.
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