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Consider the following linear equations:
ax + by + cz = 0
bx + cy + az = 0
cx + ay + bz = 0
Which of the following options correctly matches the conditions/expressions in Column I with statements in Column II?
- a)(A) → (p), (B) → (s)
- b)(A) → (q), (B) → (p)
- c)(A) → (r), (B) → (q)
- d)(A) → (s), (B) → (p)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider the following linear equations:ax + by + cz = 0bx + cy + az ...
(A) For a + b + c ≠ 0
⇒ [(a − b)2 + (b − c)2 + (c − a)2] = 0
⇒ a = b = c ≠ 0
And the given equation represents three identical planes x + y + z = 0.
(B) For |A| = 0
⇒ The solution of equation is not unique.
ax + by + cz = 0
⇒ by + cz = (b + c)x and cy + az = (c + a)x
⇒ (b + c)y + (c + a)z = (b + c)x + (c + a)x
⇒ x = y = z
(C) |A| ≠ 0; the equations have a unique solution x = y = z = 0 and three planes meet at a point.
(D) ⇒ a = b = c = 0; x, y and z can take any values, so the given equation represent the whole of three-dimensional plane.
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Consider the following linear equations:ax + by + cz = 0bx + cy + az = 0cx + ay + bz = 0Which of the following options correctly matches the conditions/expressions in Column I with statements in Column II?a)(A) → (p), (B) → (s)b)(A) → (q), (B) → (p)c)(A) → (r), (B) → (q)d)(A) → (s), (B) → (p)Correct answer is option 'C'. 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 Consider the following linear equations:ax + by + cz = 0bx + cy + az = 0cx + ay + bz = 0Which of the following options correctly matches the conditions/expressions in Column I with statements in Column II?a)(A) → (p), (B) → (s)b)(A) → (q), (B) → (p)c)(A) → (r), (B) → (q)d)(A) → (s), (B) → (p)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following linear equations:ax + by + cz = 0bx + cy + az = 0cx + ay + bz = 0Which of the following options correctly matches the conditions/expressions in Column I with statements in Column II?a)(A) → (p), (B) → (s)b)(A) → (q), (B) → (p)c)(A) → (r), (B) → (q)d)(A) → (s), (B) → (p)Correct answer is option 'C'. Can you explain this answer?.
Consider the following linear equations:ax + by + cz = 0bx + cy + az = 0cx + ay + bz = 0Which of the following options correctly matches the conditions/expressions in Column I with statements in Column II?a)(A) → (p), (B) → (s)b)(A) → (q), (B) → (p)c)(A) → (r), (B) → (q)d)(A) → (s), (B) → (p)Correct answer is option 'C'. 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 Consider the following linear equations:ax + by + cz = 0bx + cy + az = 0cx + ay + bz = 0Which of the following options correctly matches the conditions/expressions in Column I with statements in Column II?a)(A) → (p), (B) → (s)b)(A) → (q), (B) → (p)c)(A) → (r), (B) → (q)d)(A) → (s), (B) → (p)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following linear equations:ax + by + cz = 0bx + cy + az = 0cx + ay + bz = 0Which of the following options correctly matches the conditions/expressions in Column I with statements in Column II?a)(A) → (p), (B) → (s)b)(A) → (q), (B) → (p)c)(A) → (r), (B) → (q)d)(A) → (s), (B) → (p)Correct answer is option 'C'. Can you explain this answer?.
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