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Find the angle between the vectors. a = 1, −4, 1 b = 0, 5, −5 exact=?

User CDahn
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Final answer:

To find the angle between two vectors, you can use the dot product formula: a · b = |a| |b| cos(θ). Given that a = (1, -4, 1) and b = (0, 5, -5), the angle between the vectors is approximately 113.5 degrees.

Step-by-step explanation:

To find the angle between two vectors, you can use the dot product formula:

a · b = |a| |b| cos(θ)

Given that a = (1, -4, 1) and b = (0, 5, -5), the dot product of a and b is:

a · b = (1)(0) + (-4)(5) + (1)(-5) = -20

The magnitudes of the vectors are |a| = sqrt(12 + (-4)2 + 12) = sqrt(18) and |b| = sqrt(0^2 + 5^2 + (-5)^2) = sqrt(50).

Substituting these values into the formula, we have:

-20 = sqrt(18) sqrt(50) cos(θ)

Solving for θ, we get:

θ = acos(-20 / (sqrt(18) sqrt(50)))

Calculating this value gives us:

θ ≈ 113.5 degrees

User TomDLT
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