(-1,1,0). and that 11) (8 pts.) Suppose that a = b=(1,0,-2) Find two vectors v and...
7. Let u =< 2,0,3 > and v =< -1,1,0 > (a) Find || 11 (b) Find u-2u.
Question 1 (2+2+5 marks] (a) Find the angle between the vectors y =(4,0,3), v = (0,2,0). (b) Consider the subspace V (a plane) spanned by the vectors y, V. Find an orthonormal basis for the plane. (Hint: you may not need to use the full Gram-Schmidt process.) (c) Find the projection of the vector w=(1,2,3) onto the subspace Vin (b). Hence find w as a sum of two vectors wi+w, where w, is in V and w, is perpendicular to...
2. (4) Let W = span{(1,1,1), (-1,1,0)). Let v = (1,-1,2). Find the decomposition v = w; + W2, where we W and W, EW+.
5. (10pts) Let B (v1 (1,1,0), v2 (1,0,-1). v3 (0,1,-1)) be a basis of R3 Using the Gram-Schmidt process, find an orthogonal basis of R3. (You don't have to normalize the vectors.)
1. Given the vectors ū=(1,-2,-6) and v = (0,-3,4), a) Find u 6v. b) Find a unit vector in the opposite direction to ū. c) Find (ü.v)v. d) Find 11: e) Find the distance between ū and v. f) Are ū and y parallel, perpendicular, or neither? Explain. g) Verify the Triangle Inequality for ū and ū.
Suppose and. a) Calculate dot (dot product) b) Find , where is the angle between the vectors and . Are and perpindicular? c) Find a vector P that is parallel to v and a vector N that is perpendicular to v such that
Decompose v into two vectors, V, and v2, where v, is parallel to w and v2 is orthogonal to w. V= -1 + 2), w=i+2) V1 = i + V2 = ((i+O; (Simplify your answer.)
оогуппе с Score: 0 of 3 pts 13.2.71 Find two vectors parallel to v of the given length. v = (16. - 12,0); length = 15 The vector in the direction of vis 0:00
1- Two vectors are given as u = 2 – 5j and v=-{+3j. a- Find the vector 2u +3v (by calculation, not by drawing). (4 pts) b- Find the magnitudes luand il of the two vectors. (4 pts) c- Calculate the scalar product u•v. (5 pts) d- Find the angle between the vectors u and v. (6 pts) - Calculate the vector product uxv. (6 pts)
Decompose v into two vectors V, and V2, where V, is parallel to w and v2 is orthogonal to w. v=i-5j, w = 3i+j 1 29 3 7 O A. Vy=-51+ - 51, V2 = -51 5) 3 1 6 24 O B. Vy = - 51+ - 51, V2 = 51 5 3 1 8 24 OC. V = 5+ - 51, V2 = 51+ 2 2 5 43 OD. Vq = - 31+ - g), V2 = 3i+-gi