Given the vectors v and u, answer a. through d. below. v = 3i - 2k u = i + j + k a. Find the dot product of v and u. u · v = Find the length of v. |v| = (Type an exact answer, using radicals as needed.) Find the length of u. |u| = (Type an exact answer, using radicals as needed.) b. Find the cosine of the angle between v and u. cos ? = (Type an exact answer, using radicals as needed.) c. Find the scalar component of u in the direction of v. (Type an exact answer, using radicals as needed.) d. Find the vector projection of u onto v. projv u = (Type your answer in terms of i, j, and k.)
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To find the dot product of v and u, we can use the formula: $u \cdot v = (u_x \cdot v_x) + (u_y \cdot v_y) + (u_z \cdot v_z)$ So, $u \cdot v = (1 \cdot 3) + (1 \cdot 0) + (1 \cdot -2) = 3 - 2 = 1$ The length of v is: $|v| = \sqrt{(3^2) + (0^2) + (-2^2)} = Show more…
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