What is the projection of E = 2i-3j+6k onto the direction of vector F=i+2j+2k?
Correct answer: B. 8/3
- A. 1/2
- B. 8/3
- C. 3/5
- D. 5/7
- E. 7/9
Explanation
The explanation is as follows:To find the projection of vector E onto the direction ofvector F, we can use the formula: Projection of E onto F = (E dot F) / |F| First, let's calculate the dot product of E and F: E dot F =(2)(1) + (-3)(2) + (6)(2) = 2 - 6 + 12 = 8 Next, we need to find the magnitude of vector F: |F| = √(1² + 2² + 2²) = √9 = 3 Now we can calculate the projection: Projection of E onto F= (E dot F) / |F| = 8 / 3 ≈ 2.67 Therefore, the projection of vector E onto the direction ofvector F is approximately 2.67.
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Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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