How do you find the scalar and vector projections of b onto a given #a = ‹3, 2, 1›#, #b = ‹0, 1, 3›#? Precalculus Vectors in the Plane 2-D Vectors 1 Answer Vinícius Ferraz Nov 21, 2015 #proj_a(b) = (0, 1/2, 3/2)# Explanation: #proj_a (b) = v = lambda b# #v + n = a Rightarrow n = a - lambda b# #n cdot b = 0# #(a - lambda b) cdot b = 0# #a cdot b = lambda b cdot b# #lambda = (a * b)/(b * b) = (0 + 2 + 3)/(0 + 1 + 9) = 5/10 = 1/2# #v = 1/2 b = (0, 1/2, 3/2)# Answer link Related questions How do I find the magnitude of a vector? How do I find the resultant of vectors? How can vectors be parallel? What is meant by the initial point of a vector? What is the definition of a vector? How do I multiply a vector by a scalar? What are common mistakes students make with 2-D vectors? What is the terminal point of a vector? How do you find the magnitude and direction for U: magnitude 140, bearing 160° V: magnitude 200,... How do you write vector U = 6 and Theta = 45 degrees in cartesian form? See all questions in 2-D Vectors Impact of this question 1409 views around the world You can reuse this answer Creative Commons License