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Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?
- a)6, 2
- b)1, 3
- c)3, 1
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4...
LM = (2 − 1)2 +(3 − 2)2 + (m − 3)2 = 2
⇒ 1 + 1 + (m − 3)2 = 2
⇒ (m − 3)2 = 0
⇒ m = 3
Similarly, by LK = 2, we can get n = 1.
Most Upvoted Answer
Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4...
To find the coordinates of points L, M, N, and K, we can use the fact that a parallelogram has opposite sides that are equal in length and parallel.
First, let's find the vector representing the direction from O to P:
OP = (4, 6, 2m) - (0, 0, 0) = (4, 6, 2m)
Next, let's find the vector representing the direction from O to Q:
OQ = (2, 0, 2n) - (0, 0, 0) = (2, 0, 2n)
Since LK and LM are parallel to OP, their directions will be the same as OP. Therefore, we can say that the vector representing the direction from O to L is:
OL = OP = (4, 6, 2m)
Similarly, the vector representing the direction from O to M is:
OM = OP = (4, 6, 2m)
Since MN and NK are parallel to OQ, their directions will be the same as OQ. Therefore, we can say that the vector representing the direction from O to N is:
ON = OQ = (2, 0, 2n)
And the vector representing the direction from O to K is:
OK = OQ = (2, 0, 2n)
Now, we can find the coordinates of points L, M, N, and K by adding the respective vectors to the coordinates of O:
Coordinates of L: (0, 0, 0) + (4, 6, 2m) = (4, 6, 2m)
Coordinates of M: (0, 0, 0) + (4, 6, 2m) = (4, 6, 2m)
Coordinates of N: (0, 0, 0) + (2, 0, 2n) = (2, 0, 2n)
Coordinates of K: (0, 0, 0) + (2, 0, 2n) = (2, 0, 2n)
Therefore, the coordinates of points L, M, N, and K are (4, 6, 2m), (4, 6, 2m), (2, 0, 2n), and (2, 0, 2n), respectively.
First, let's find the vector representing the direction from O to P:
OP = (4, 6, 2m) - (0, 0, 0) = (4, 6, 2m)
Next, let's find the vector representing the direction from O to Q:
OQ = (2, 0, 2n) - (0, 0, 0) = (2, 0, 2n)
Since LK and LM are parallel to OP, their directions will be the same as OP. Therefore, we can say that the vector representing the direction from O to L is:
OL = OP = (4, 6, 2m)
Similarly, the vector representing the direction from O to M is:
OM = OP = (4, 6, 2m)
Since MN and NK are parallel to OQ, their directions will be the same as OQ. Therefore, we can say that the vector representing the direction from O to N is:
ON = OQ = (2, 0, 2n)
And the vector representing the direction from O to K is:
OK = OQ = (2, 0, 2n)
Now, we can find the coordinates of points L, M, N, and K by adding the respective vectors to the coordinates of O:
Coordinates of L: (0, 0, 0) + (4, 6, 2m) = (4, 6, 2m)
Coordinates of M: (0, 0, 0) + (4, 6, 2m) = (4, 6, 2m)
Coordinates of N: (0, 0, 0) + (2, 0, 2n) = (2, 0, 2n)
Coordinates of K: (0, 0, 0) + (2, 0, 2n) = (2, 0, 2n)
Therefore, the coordinates of points L, M, N, and K are (4, 6, 2m), (4, 6, 2m), (2, 0, 2n), and (2, 0, 2n), respectively.
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Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?a)6, 2b)1, 3c)3, 1d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?a)6, 2b)1, 3c)3, 1d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?a)6, 2b)1, 3c)3, 1d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?a)6, 2b)1, 3c)3, 1d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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Solutions for Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?a)6, 2b)1, 3c)3, 1d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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