What is the angle between the two 3D vectors and ?
Answer and explanation
Correct answer: B. ( radians)
- Step 1: Compute dot product: .
- Step 2: Compute magnitudes: , .
- Step 3: \cos\theta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}| = \frac{1}{\sqrt{2} \times \sqrt{2}} = \frac{1}{2}.
- Step 4: radians.
Answer
60 degrees (pi/3 radians).
Why not the others: '' is for ; '' would require orthogonal dot product 0.
Practise more Calculus and Mathematical Analysis.
Free questions with an explanation for every one, and full timed General Education Diploma (GED Oman) mock tests.
More Calculus and Mathematical Analysis questions
- Evaluate the trigonometric limit: lim (x -> 0) [sin(7x) / (2x)].
- Find the derivative of the rational function f(x) = (3x - 5) / (2x + 1) for x != -1/2.
- What is the slope of the tangent line to the curve y = 2x^3 - 5x^2 + 4 at x = 2?
- Determine the indefinite integral: integral of (6x^2 - 4x + 5) dx.
- Evaluate the definite integral: integral from 0 to 3 of (4x + 1) dx.
- Find the local maximum of the polynomial function f(x) = -x^3 + 3x + 2.