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Can you explain the answer of this question below:
The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:
- A:1 , 0 , -2/3
- B:3/√13, 0, -2/√13
- C:3/4, 0, -2/4
- D:-3/√12, 0, -2/√13
The answer is b.
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Explanation:
Finding the midpoint of AC:
- Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)
- Midpoint of AC: ((-2 + 0)/2, (3 + 5)/2, (6 + 8)/2) = (-1, 4, 7)
Finding the vector BE:
- Vector BE = Vector E - Vector B
- Vector E = Midpoint of AC = (-1, 4, 7)
- Vector B = (-4, 4, 9)
- Vector BE = (-1 + 4, 4 - 4, 7 - 9) = (3, 0, -2)
Calculating the direction cosines of BE:
- Direction cosines (l, m, n) = (A, B, C) / sqrt(A^2 + B^2 + C^2)
- l = 3/sqrt(3^2 + 0^2 + (-2)^2) = 3/sqrt(13)
- m = 0/sqrt(13) = 0
- n = -2/sqrt(13) = -2/sqrt(13) = -2/13
Therefore, the direction cosines of the median BE are 3/13, 0, -2/13, which matches option B.
Finding the midpoint of AC:
- Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)
- Midpoint of AC: ((-2 + 0)/2, (3 + 5)/2, (6 + 8)/2) = (-1, 4, 7)
Finding the vector BE:
- Vector BE = Vector E - Vector B
- Vector E = Midpoint of AC = (-1, 4, 7)
- Vector B = (-4, 4, 9)
- Vector BE = (-1 + 4, 4 - 4, 7 - 9) = (3, 0, -2)
Calculating the direction cosines of BE:
- Direction cosines (l, m, n) = (A, B, C) / sqrt(A^2 + B^2 + C^2)
- l = 3/sqrt(3^2 + 0^2 + (-2)^2) = 3/sqrt(13)
- m = 0/sqrt(13) = 0
- n = -2/sqrt(13) = -2/sqrt(13) = -2/13
Therefore, the direction cosines of the median BE are 3/13, 0, -2/13, which matches option B.
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Can you explain the answer of this question below:The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:A:1 , 0 , -2/3B:3/√13, 0, -2/√13C:3/4, 0, -2/4D:-3/√12, 0, -2/√13The answer is b.
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Can you explain the answer of this question below:The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:A:1 , 0 , -2/3B:3/√13, 0, -2/√13C:3/4, 0, -2/4D:-3/√12, 0, -2/√13The answer is b. for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below:The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:A:1 , 0 , -2/3B:3/√13, 0, -2/√13C:3/4, 0, -2/4D:-3/√12, 0, -2/√13The answer is b. covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:A:1 , 0 , -2/3B:3/√13, 0, -2/√13C:3/4, 0, -2/4D:-3/√12, 0, -2/√13The answer is b..
Can you explain the answer of this question below:The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:A:1 , 0 , -2/3B:3/√13, 0, -2/√13C:3/4, 0, -2/4D:-3/√12, 0, -2/√13The answer is b. for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below:The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:A:1 , 0 , -2/3B:3/√13, 0, -2/√13C:3/4, 0, -2/4D:-3/√12, 0, -2/√13The answer is b. covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:A:1 , 0 , -2/3B:3/√13, 0, -2/√13C:3/4, 0, -2/4D:-3/√12, 0, -2/√13The answer is b..
Solutions for Can you explain the answer of this question below:The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:A:1 , 0 , -2/3B:3/√13, 0, -2/√13C:3/4, 0, -2/4D:-3/√12, 0, -2/√13The answer is b. in English & in Hindi are available as part of our courses for JEE.
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