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The points whose position vectors are 2i+3j+4k, 3i+4j+2k, 4i+2j+3k, then they are
- a)vertices of right angled triangle
- b)vertices of an isosceles triangle
- c)vertices of an equilateral triangle
- d)collinear
Correct answer is option 'C'. Can you explain this answer?
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The points whose position vectors are 2i+3j+4k, 3i+4j+2k, 4i+2j+3k, th...
Given points P(2,3,4), Q(3,4,2), R(4,2,3)
To check if the given points form an equilateral triangle, we need to check if the distance between each pair of points is equal.
Using the distance formula, we can find the distance between P and Q, Q and R, and R and P:
|PQ| = √[(3-2)² + (4-3)² + (2-4)²] = √10
|QR| = √[(4-3)² + (2-4)² + (3-2)²] = √10
|RP| = √[(2-4)² + (3-2)² + (4-2)²] = √10
Since all three distances are equal, the given points form an equilateral triangle. Therefore, the correct answer is option C.
To check if the given points form an equilateral triangle, we need to check if the distance between each pair of points is equal.
Using the distance formula, we can find the distance between P and Q, Q and R, and R and P:
|PQ| = √[(3-2)² + (4-3)² + (2-4)²] = √10
|QR| = √[(4-3)² + (2-4)² + (3-2)²] = √10
|RP| = √[(2-4)² + (3-2)² + (4-2)²] = √10
Since all three distances are equal, the given points form an equilateral triangle. Therefore, the correct answer is option C.
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The points whose position vectors are 2i+3j+4k, 3i+4j+2k, 4i+2j+3k, th...
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The points whose position vectors are 2i+3j+4k, 3i+4j+2k, 4i+2j+3k, then they area)vertices of right angled triangleb)vertices of an isosceles trianglec)vertices of an equilateral triangled)collinearCorrect answer is option 'C'. Can you explain this answer?
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