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The angle between the vectors 3i+j+2k and 2i-2j+4k is
- a)cos⁻1(2/√7)
- b)sin⁻1(2/√7)
- c)cos⁻1(2/√5)
- d)sin⁻1(1/√7)
Correct answer is option 'B'. Can you explain this answer?
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The angle between the vectors 3i+j+2k and 2i-2j+4k isa)cos⁻1(2/&...
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The angle between the vectors 3i+j+2k and 2i-2j+4k isa)cos⁻1(2/&...
To find the angle between two vectors, we use the formula:
cosθ = (a · b) / (|a| |b|)
where a and b are the two vectors, · represents the dot product, and |a| and |b| represent the magnitudes of the vectors.
Using this formula, we have:
a = 3i + j + 2k
b = 2i - 2j + 4k
a · b = (3i + j + 2k) · (2i - 2j + 4k)
= 6i^2 - 6j^2 + 8k^2
= 6(1) - 6(1) + 8(1)
= 8
|a| = sqrt(3^2 + 1^2 + 2^2) = sqrt(14)
|b| = sqrt(2^2 + (-2)^2 + 4^2) = sqrt(24)
Substituting into the formula, we get:
cosθ = (a · b) / (|a| |b|)
= 8 / (sqrt(14) sqrt(24))
= 2 / sqrt(21)
Therefore, the angle between the vectors is:
θ = cos^-1(2 / sqrt(21)) ≈ 36.87 degrees (rounded to two decimal places)
cosθ = (a · b) / (|a| |b|)
where a and b are the two vectors, · represents the dot product, and |a| and |b| represent the magnitudes of the vectors.
Using this formula, we have:
a = 3i + j + 2k
b = 2i - 2j + 4k
a · b = (3i + j + 2k) · (2i - 2j + 4k)
= 6i^2 - 6j^2 + 8k^2
= 6(1) - 6(1) + 8(1)
= 8
|a| = sqrt(3^2 + 1^2 + 2^2) = sqrt(14)
|b| = sqrt(2^2 + (-2)^2 + 4^2) = sqrt(24)
Substituting into the formula, we get:
cosθ = (a · b) / (|a| |b|)
= 8 / (sqrt(14) sqrt(24))
= 2 / sqrt(21)
Therefore, the angle between the vectors is:
θ = cos^-1(2 / sqrt(21)) ≈ 36.87 degrees (rounded to two decimal places)
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The angle between the vectors 3i+j+2k and 2i-2j+4k isa)cos⁻1(2/√7)b)sin⁻1(2/√7)c)cos⁻1(2/√5)d)sin⁻1(1/√7)Correct answer is option 'B'. Can you explain this answer?
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The angle between the vectors 3i+j+2k and 2i-2j+4k isa)cos⁻1(2/√7)b)sin⁻1(2/√7)c)cos⁻1(2/√5)d)sin⁻1(1/√7)Correct answer is option 'B'. 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 the vectors 3i+j+2k and 2i-2j+4k isa)cos⁻1(2/√7)b)sin⁻1(2/√7)c)cos⁻1(2/√5)d)sin⁻1(1/√7)Correct answer is option 'B'. 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 the vectors 3i+j+2k and 2i-2j+4k isa)cos⁻1(2/√7)b)sin⁻1(2/√7)c)cos⁻1(2/√5)d)sin⁻1(1/√7)Correct answer is option 'B'. Can you explain this answer?.
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