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The angle between two lines whose direction ratios are 1,2,1 and 2,-3,4 is:
- a)30°
- b)60°
- c)90°
- d)45°
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The angle between two lines whose direction ratios are 1,2,1 and 2,-3,...
Cosx =( i+2j+k).(2i-3j+4k)/ √1+4+1 × √4+9+16
cosx= 2-6+4/√1+4+1 × √4+9+16
cosx = 0/√1+4+1 × √4+9+16
cosx = 0
therfore
x = 90
cosx= 2-6+4/√1+4+1 × √4+9+16
cosx = 0/√1+4+1 × √4+9+16
cosx = 0
therfore
x = 90
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Community Answer
The angle between two lines whose direction ratios are 1,2,1 and 2,-3,...
Calculating the angle between two lines:
To find the angle between two lines, we can use the formula:
cosθ = (a1 * a2 + b1 * b2 + c1 * c2) / (sqrt(a1^2 + b1^2 + c1^2) * sqrt(a2^2 + b2^2 + c2^2))
Where a1, b1, c1 are the direction ratios of the first line and a2, b2, c2 are the direction ratios of the second line.
Given direction ratios:
Line 1: 1, 2, 1
Line 2: 2, -3, 4
Calculating the dot product of direction ratios:
a1 * a2 = 1 * 2 = 2
b1 * b2 = 2 * -3 = -6
c1 * c2 = 1 * 4 = 4
Calculating the magnitude of direction ratios:
sqrt(a1^2 + b1^2 + c1^2) = sqrt(1^2 + 2^2 + 1^2) = sqrt(6) = √6
sqrt(a2^2 + b2^2 + c2^2) = sqrt(2^2 + (-3)^2 + 4^2) = sqrt(29)
Substitute the values in the formula:
cosθ = (2 - 6 + 4) / (√6 * √29)
cosθ = 0 / (√6 * √29) = 0
Calculating the angle:
Since cosθ = 0, the angle between the two lines is 90 degrees (θ = 90°).
Therefore, the correct answer is option C) 90.
To find the angle between two lines, we can use the formula:
cosθ = (a1 * a2 + b1 * b2 + c1 * c2) / (sqrt(a1^2 + b1^2 + c1^2) * sqrt(a2^2 + b2^2 + c2^2))
Where a1, b1, c1 are the direction ratios of the first line and a2, b2, c2 are the direction ratios of the second line.
Given direction ratios:
Line 1: 1, 2, 1
Line 2: 2, -3, 4
Calculating the dot product of direction ratios:
a1 * a2 = 1 * 2 = 2
b1 * b2 = 2 * -3 = -6
c1 * c2 = 1 * 4 = 4
Calculating the magnitude of direction ratios:
sqrt(a1^2 + b1^2 + c1^2) = sqrt(1^2 + 2^2 + 1^2) = sqrt(6) = √6
sqrt(a2^2 + b2^2 + c2^2) = sqrt(2^2 + (-3)^2 + 4^2) = sqrt(29)
Substitute the values in the formula:
cosθ = (2 - 6 + 4) / (√6 * √29)
cosθ = 0 / (√6 * √29) = 0
Calculating the angle:
Since cosθ = 0, the angle between the two lines is 90 degrees (θ = 90°).
Therefore, the correct answer is option C) 90.
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The angle between two lines whose direction ratios are 1,2,1 and 2,-3,4 is:a)30°b)60°c)90°d)45°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 The angle between two lines whose direction ratios are 1,2,1 and 2,-3,4 is:a)30°b)60°c)90°d)45°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 The angle between two lines whose direction ratios are 1,2,1 and 2,-3,4 is:a)30°b)60°c)90°d)45°Correct answer is option 'C'. Can you explain this answer?.
The angle between two lines whose direction ratios are 1,2,1 and 2,-3,4 is:a)30°b)60°c)90°d)45°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 The angle between two lines whose direction ratios are 1,2,1 and 2,-3,4 is:a)30°b)60°c)90°d)45°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 The angle between two lines whose direction ratios are 1,2,1 and 2,-3,4 is:a)30°b)60°c)90°d)45°Correct answer is option 'C'. Can you explain this answer?.
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