Final answer:
By evaluating the expression;
D) V.W= <27, -18, 8>.
Step-by-step explanation:
To find the dot product of vectors V and W, denoted as V·W, we perform the operation on their respective components. V=<3,3,−8> and W=<9,−6,−1>. The dot product of two vectors is calculated by multiplying their corresponding components and then summing the results. Therefore, V·W = (3 * 9) + (3 * -6) + (-8 * -1) = 27 - 18 + 8 = 27 - 18 + 8 = <27, -18, 8>.(D)
This result aligns with the given option D). The dot product of vectors helps in determining the projection of one vector onto another and is crucial in various mathematical and physical applications, measuring the similarity or perpendicularity of vectors. In this case, the result <27, -18, 8> signifies the value of the dot product between V and W, indicating their relationship in terms of direction and magnitude.
Understanding vector operations like dot products assists in comprehending vector spaces, linear algebra, and applications in physics, engineering, and computer science. The dot product's value indicates the degree of alignment or opposition between two vectors, crucial for vector analysis in multidimensional spaces. Thus, the final answer of <27, -18, 8> accurately represents the dot product V·W of the given vectors V and W.