A. B. Let the position vecor be R(t) = (-t, 4 cos (2t), 4 sin(2t)). Compute the principal unit normal vector N(t). (-1,-8 sin(2t), 8 cos(2t)) √65 (-t, 4 cos(2t), 4 sin(2t)) √65 O C. (-1,-8 sin(2t), 8 cos(2t)) D. (0,- (cos(2t)),- (sin(2t))) E. (0,- (16 cos(2t)),-16 sin(2t)) 65

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A: i+2j+xkTo Find: Value of x so that the vector makes an angle of π4 with the positive z axis.

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Q: I need help with this problem and an explanation for the solution described below. (Calculus 3:…

A: Step 1:

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A: Given rt=e2tcosti+e2tsintj+2k

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Q: [1 [4] Determine if the vectors v₁ = 2, 12 vi 2,√2 = 5, and v3 L3. L6. independent. = 8 are linearly…

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A: We can solve this using spherical co-ordinate matrix