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The points with position vectors 10î+3ĵ, 12î-5ĵ and aî+11ĵ are collinear if a =
- a)-8
- b)4
- c)12
- d)8
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The points with position vectors 10î+3ĵ, 12î-5ĵ...
Given, A = (10i + 3j)
B = (12i - 5j)
C = (ai + 11j)
AB = 2i - 8j
AC = (a - 10)i + 8j
AB and AC are collinear
⇒ 2/(a - 10) = -8/8
⇒ 2 = 10 - a
⇒ a = 8
B = (12i - 5j)
C = (ai + 11j)
AB = 2i - 8j
AC = (a - 10)i + 8j
AB and AC are collinear
⇒ 2/(a - 10) = -8/8
⇒ 2 = 10 - a
⇒ a = 8
Most Upvoted Answer
The points with position vectors 10î+3ĵ, 12î-5ĵ...
Explanation:
- Let's assume that the three points are collinear.
- So, the slope of the line passing through the first two points should be equal to the slope of the line passing through the second and third points.
- Let the first two points with position vectors 10i + 3j and 12i - 5j be A and B respectively.
- The slope of line AB is given by (y2-y1)/(x2-x1) = (-5-3)/(12-10) = -4/1 = -4
- Let the third point with position vector ai + 11j be C.
- The slope of line BC is given by (y2-y1)/(x2-x1) = (11-(-5))/(a-12) = 16/(a-12)
- Since the points are collinear, the slopes of both lines are equal.
- Therefore, -4 = 16/(a-12)
- Multiplying both sides by (a-12), we get -4a + 48 = 16
- So, -4a = -32, which gives a = 8.
- Therefore, option D is the correct answer.
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The points with position vectors 10î+3ĵ, 12î-5ĵ...
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The points with position vectors 10î+3ĵ, 12î-5ĵ and aî+11ĵ are collinear if a =a)-8b)4c)12d)8Correct answer is option 'D'. Can you explain this answer?
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The points with position vectors 10î+3ĵ, 12î-5ĵ and aî+11ĵ are collinear if a =a)-8b)4c)12d)8Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The points with position vectors 10î+3ĵ, 12î-5ĵ and aî+11ĵ are collinear if a =a)-8b)4c)12d)8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The points with position vectors 10î+3ĵ, 12î-5ĵ and aî+11ĵ are collinear if a =a)-8b)4c)12d)8Correct answer is option 'D'. Can you explain this answer?.
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