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The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an anlge π/4 with the plane y–z+5=0 are:
  • a)
     2 √3 , 1, –1
  • b)
    2, √2 , – √2
  • c)
    2, –1, 1
  • d)
    √2 , 1, –1
Correct answer is option 'B,D'. Can you explain this answer?
Verified Answer
The direction ratios of normal to the plane through the points (0, &nd...
Let the equation of plane be a(x – 0) + b(y + 1) + c(z – 0) = 0 It passes through (0,0,1) then
b + c = 0 ...(1)

⇒ a2 = –2bc and b = –c
we get a2 = 2c2

⇒ direction ratio (a, b, c) = (√2, -1, 1) or  (√2, 1, -1)
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Most Upvoted Answer
The direction ratios of normal to the plane through the points (0, &nd...
0, 0), (1, 0, 0), and (0, 1, 0) are given by the cross product of the vectors formed by subtracting one point from another.

The vector formed by subtracting (0, 0, 0) from (1, 0, 0) is (1, 0, 0). The vector formed by subtracting (0, 0, 0) from (0, 1, 0) is (0, 1, 0).

Taking the cross product of these two vectors:

(1, 0, 0) × (0, 1, 0) = (0 * 0 - 1 * 1, -1 * 0 - 0 * 0, 1 * 1 - 0 * 0)
= (0, 0, 1)

Therefore, the direction ratios of the normal to the plane through the points (0, 0, 0), (1, 0, 0), and (0, 1, 0) are (0, 0, 1).
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The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) andmaking an anlgeπ/4with the plane y–z+5=0 are:a)2 √3 , 1, –1b)2, √2 , – √2c)2, –1, 1d)√2 , 1, –1Correct answer is option 'B,D'. Can you explain this answer?
Question Description
The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) andmaking an anlgeπ/4with the plane y–z+5=0 are:a)2 √3 , 1, –1b)2, √2 , – √2c)2, –1, 1d)√2 , 1, –1Correct answer is option 'B,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 direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) andmaking an anlgeπ/4with the plane y–z+5=0 are:a)2 √3 , 1, –1b)2, √2 , – √2c)2, –1, 1d)√2 , 1, –1Correct answer is option 'B,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 direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) andmaking an anlgeπ/4with the plane y–z+5=0 are:a)2 √3 , 1, –1b)2, √2 , – √2c)2, –1, 1d)√2 , 1, –1Correct answer is option 'B,D'. Can you explain this answer?.
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