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The vertices of a triangle are A(1, 1, 2), B(4, 3, 1) and C(2, 3, 5). A vector representing the internal bisector of the angle A is
- a)Î +j^+2K^
- b)2i^–2j^+k^
- c)2i^+2j^–K^
- d)2i^+2j^+k^
Correct answer is option 'D'. Can you explain this answer?
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The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A...
To find the internal bisector of angle A, we can use the formula for a vector representing the internal bisector of two vectors.
Let vector AB = (x1, y1, z1) and vector AC = (x2, y2, z2).
Then the vector representing the internal bisector of A is given by:
(x1 * |AC| + x2 * |AB|, y1 * |AC| + y2 * |AB|, z1 * |AC| + z2 * |AB|) / (|AC| + |AB|)
First, let's find vector AB and vector AC:
Vector AB = B - A = (4-1, 3-1, 1-2) = (3, 2, -1)
Vector AC = C - A = (2-1, 3-1, 5-2) = (1, 2, 3)
Next, let's find the magnitudes of AB and AC:
|AB| = √(3^2 + 2^2 + (-1)^2) = √(9 + 4 + 1) = √14
|AC| = √(1^2 + 2^2 + 3^2) = √(1 + 4 + 9) = √14
Now we can substitute the values into the formula:
(x1 * |AC| + x2 * |AB|, y1 * |AC| + y2 * |AB|, z1 * |AC| + z2 * |AB|) / (|AC| + |AB|)
= (3 * √14 + 1 * √14, 2 * √14 + 2 * √14, -1 * √14 + 3 * √14) / (√14 + √14)
= (4√14, 4√14, 2√14) / 2√14
= (2, 2, 1)
Therefore, the vector representing the internal bisector of angle A is (2, 2, 1).
Let vector AB = (x1, y1, z1) and vector AC = (x2, y2, z2).
Then the vector representing the internal bisector of A is given by:
(x1 * |AC| + x2 * |AB|, y1 * |AC| + y2 * |AB|, z1 * |AC| + z2 * |AB|) / (|AC| + |AB|)
First, let's find vector AB and vector AC:
Vector AB = B - A = (4-1, 3-1, 1-2) = (3, 2, -1)
Vector AC = C - A = (2-1, 3-1, 5-2) = (1, 2, 3)
Next, let's find the magnitudes of AB and AC:
|AB| = √(3^2 + 2^2 + (-1)^2) = √(9 + 4 + 1) = √14
|AC| = √(1^2 + 2^2 + 3^2) = √(1 + 4 + 9) = √14
Now we can substitute the values into the formula:
(x1 * |AC| + x2 * |AB|, y1 * |AC| + y2 * |AB|, z1 * |AC| + z2 * |AB|) / (|AC| + |AB|)
= (3 * √14 + 1 * √14, 2 * √14 + 2 * √14, -1 * √14 + 3 * √14) / (√14 + √14)
= (4√14, 4√14, 2√14) / 2√14
= (2, 2, 1)
Therefore, the vector representing the internal bisector of angle A is (2, 2, 1).
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The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A vector representing the internalbisector of the angle A isa)Î +j^+2K^b)2i^–2j^+k^c)2i^+2j^–K^d)2i^+2j^+k^Correct answer is option 'D'. Can you explain this answer?
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The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A vector representing the internalbisector of the angle A isa)Î +j^+2K^b)2i^–2j^+k^c)2i^+2j^–K^d)2i^+2j^+k^Correct 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 The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A vector representing the internalbisector of the angle A isa)Î +j^+2K^b)2i^–2j^+k^c)2i^+2j^–K^d)2i^+2j^+k^Correct 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 The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A vector representing the internalbisector of the angle A isa)Î +j^+2K^b)2i^–2j^+k^c)2i^+2j^–K^d)2i^+2j^+k^Correct answer is option 'D'. Can you explain this answer?.
The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A vector representing the internalbisector of the angle A isa)Î +j^+2K^b)2i^–2j^+k^c)2i^+2j^–K^d)2i^+2j^+k^Correct 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 The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A vector representing the internalbisector of the angle A isa)Î +j^+2K^b)2i^–2j^+k^c)2i^+2j^–K^d)2i^+2j^+k^Correct 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 The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A vector representing the internalbisector of the angle A isa)Î +j^+2K^b)2i^–2j^+k^c)2i^+2j^–K^d)2i^+2j^+k^Correct answer is option 'D'. Can you explain this answer?.
Solutions for The vertices of a triangle are A(1, 1, 2), B(4, 3, 1)and C(2, 3, 5). A vector representing the internalbisector of the angle A isa)Î +j^+2K^b)2i^–2j^+k^c)2i^+2j^–K^d)2i^+2j^+k^Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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