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Answer: c
Explanation: The dot product the vector is 8. Angle of separation is cos θ = 8/ (7.07 X 3)= 0.377 and θ = cos-1(0.377) = 67.8.
Answer: c
Explanation: The dot product the vector is 8. Angle of separation is cos θ = 8/ (7.07 X 3)
= 0.377 and θ = cos-1
(0.377) = 67.8.
To find the angular separation between the two vectors ( A = 4i + 3j + 5k ) and ( B = i – 2j + 2k ), we can use the formula for the cosine of the angle ( theta ) between two vectors:
[
cos(theta) = frac{A cdot B}{|A| |B|}
]
1. Calculate the dot product ( A cdot B ):
[
A cdot B = (4)(1) + (3)(-2) + (5)(2) = 4 – 6 + 10 = 8
]
2. Calculate the magnitudes of ( A ) and ( B ):
[
|A| = sqrt{4^2 + 3^2 + 5^2} = sqrt{16 + 9 + 25} = sqrt{50} = 5sqrt{2}
]
[
|B| = sqrt{1^2 + (-2)^2 + 2^2} = sqrt{1 + 4 + 4} = sqrt{9} = 3
]
3. Substituting into the cosine formula:
[
cos(theta) = frac{8}{(5sqrt{2})(3)}