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The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k is
- a)[(√115)/(√14)(√194)]
- b)[(51)/(√14)(√144)]
- c)[(√64)/(√14)(√194)]
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(...
To find the sine of the angle between two vectors, we can use the formula:
sin θ = ||A x B|| / ||A|| ||B||
where A and B are the given vectors, and A x B is their cross product.
First, let's find the cross product of the two vectors:
A x B = (2*-5 - (-1*5))i - (3*-5 - 1*12)j + (3*5 - 2*12)k
= -10i - 27j - 9k
Next, let's find the magnitudes of the two vectors:
||A|| = √(3^2 + 2^2 + (-1)^2) = √14
||B|| = √(12^2 + 5^2 + (-5)^2) = √194
Finally, we can plug everything into the formula for the sine of the angle:
sin θ = ||A x B|| / ||A|| ||B||
= ||-10i - 27j - 9k|| / (√14)(√194)
= √(10^2 + 27^2 + 9^2) / (√14)(√194)
= √874 / (√14)(√194)
This cannot be simplified further, so the answer is:
a) √874 / (√14)(√194)
sin θ = ||A x B|| / ||A|| ||B||
where A and B are the given vectors, and A x B is their cross product.
First, let's find the cross product of the two vectors:
A x B = (2*-5 - (-1*5))i - (3*-5 - 1*12)j + (3*5 - 2*12)k
= -10i - 27j - 9k
Next, let's find the magnitudes of the two vectors:
||A|| = √(3^2 + 2^2 + (-1)^2) = √14
||B|| = √(12^2 + 5^2 + (-5)^2) = √194
Finally, we can plug everything into the formula for the sine of the angle:
sin θ = ||A x B|| / ||A|| ||B||
= ||-10i - 27j - 9k|| / (√14)(√194)
= √(10^2 + 27^2 + 9^2) / (√14)(√194)
= √874 / (√14)(√194)
This cannot be simplified further, so the answer is:
a) √874 / (√14)(√194)
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Community Answer
The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(...
Let
For two vectors A and B,θ
be the angle between the two vectors|A|*|B|*cos
θ=A.B
|A|=
√(3^2+2^2+(-1)^2)=
√14
|B|=
√(12^2+5^2+(-5)^2)=
√194
A.B= 3*12+2*5+(-1)*(-5)=51
|A|*|B|*cos
θ=A.B
√14*
√194*cos
θ
=51
cos
θ=51/(
√14*
√194)
sin
θ=
√(14*194-51^2)/
√14*
√194
sin
θ=[(
√115)/(
√14*
√194)]
Hence Proved.
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The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(√115)/(√14)(√194)]b)[(51)/(√14)(√144)]c)[(√64)/(√14)(√194)]d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(√115)/(√14)(√194)]b)[(51)/(√14)(√144)]c)[(√64)/(√14)(√194)]d)none of theseCorrect answer is option 'A'. 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 sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(√115)/(√14)(√194)]b)[(51)/(√14)(√144)]c)[(√64)/(√14)(√194)]d)none of theseCorrect answer is option 'A'. 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 sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(√115)/(√14)(√194)]b)[(51)/(√14)(√144)]c)[(√64)/(√14)(√194)]d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(√115)/(√14)(√194)]b)[(51)/(√14)(√144)]c)[(√64)/(√14)(√194)]d)none of theseCorrect answer is option 'A'. 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 sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(√115)/(√14)(√194)]b)[(51)/(√14)(√144)]c)[(√64)/(√14)(√194)]d)none of theseCorrect answer is option 'A'. 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 sine of the angle between the vectors 3i+2j-k and 12i+5j-5k isa)[(√115)/(√14)(√194)]b)[(51)/(√14)(√144)]c)[(√64)/(√14)(√194)]d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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