Given the vectors v and u, find the dot product of v and u. Find the length of v. Find the length of u. Find the cosine of the angle between v and u. Find the scalar component of v. Find the direction of v. Find the vector projection of v onto u.
Added by Kristine T.
Step 1
Dot product of v and u: The dot product of two vectors v and u is given by v.u = |v||u|cosθ, where |v| and |u| are the magnitudes of the vectors and θ is the angle between them. Since u is a scalar, we can write it as u = |u|, and the dot product becomes v.u = (2i Show more…
Show all steps
Close
Your feedback will help us improve your experience
Naresh Bagrecha and 81 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Given the vectors v and u, answer a. through d. below. v = 6i + 2j - 3k u = 3i + 4j a. Find the dot product of v and u. (u · v) b. Find the length of v. (|v|) c. Find the length of u. (|u|) d. Find the cosine of the angle between v and u. e. Find the scalar component of u in the direction of v. f. Find the vector projection of u onto v.
Melissa M.
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| = Find the length of u. |u| = b. Find the cosine of the angle between v and u. cos θ = c. Find the scalar component of u in the direction of v. d. Find the vector projection of u onto v. projv u =
Sri K.
v = 8i - 5k. u = i + j + k a. Find the dot product of v and u. u · v = Find the length of |v| = Find the length of |u| b. Find the cosine of the angle between v and u cos θ = c. Find the scalar component of u in the direction of v. d. Find the vector projection of u onto v.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD