Find the projection of Y = 4i - 6j + 12k onto the direction of vector Z = 2i + 4j + 4k.
Correct answer: B. 16/3
- A. 7/3
- B. 16/3
- C. 3/7
- D. 9/7
- E. 5/9
Explanation
Vector Y is in 4th xy quadrantY = √(4^2 + 6^2 + 12^2)Y = √(16 + 36 + 144)Y = √196Y = 14 (Y.Z)/Y = ( 4*2 + 6*4 + 12*4)/14 = 80/14 = 5.7 = 16/3 Hence, option B is correct.
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About Scalar Product
The scalar product of two vectors is A dot B equals AB cos theta, producing a scalar determined by their magnitudes and included angle. Applications include work done and projection of one vector on another, with perpendicular vectors giving zero and the scalar product distinguished from the vector product.
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