Given vectors ü = (-1,5), i = 3i – 4j, w = (2,7), find: (2pts each) a. 3ū + 20 - w b. llull c. A unit vector in the direction of v d. (ü + ). W e. The angle between ï and W. Write your final answer in degrees rounded to 3 decimal places.
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12 + 69, then find the following: A. 2w - 3ū B. ||2u - 57 C. v. W D. the angle between ü and v E. the direction angle of vector w F. (3 +70).ü G. a vector in the same direction as ū with magnitude of 12 H. a vector orthogonal to vector v with magnitude of 7 I. any vector that is orthogonal...
1. Let ū= (2,4,-1), v = (3.-3,-1) (a) Compute: x ū (b) Compute: ü x 7 (c) Is the cross product commutative? If not, what is it instead? 2. Let A = (7, -11,3), B = (1,9, -3), C = (-6,3, -2), D= (0,-8, 12), E = (1, -13,2) (a) Give the vector equation of a line passing through the points A, B. (b) Find the equation of the plane containing the points C,D,E. (c) Find the point of intersection...
(a) Suppose that ū,ū e R". Show u2u-22||2 2해2 (b) (The Pythagoras Theorem) Suppose that u, v e R". Show that ul if and only if ||ü + 해2 (c) Let W be a subspace of R" with an orthogonal basis {w1, ..., w,} and let {ö1, ..., ūg} 22 orthogonal basis for W- (i) Explain why{w1, ..., üp, T1, .., T,} is an (ii Explain why the set in (i) spans R". (iii Show that dim(W) + dim(W1) be...
(1 point) Let u= (3, 2) and v = (1,5). Then u +v=< 7 U-v=< -30 =< u. V = and || 0 ||
Let ū = [1,-1, 1], v = (-2,-1, 3] and W = (-1, 2, 2). Find (u x D) • w O Does not exist 7 -14 10
Exercise 1. Let v = 2 ER3. Recall that the transposed vector u is ū written in row form, 3 that is, of = [1 2 3]. It can be seen as a 1 x 3 matrix. For every vector R3, set f(w) = 1 WER. (i) Show that f: R3 → R defines a linear transformation. (ii) Show that f(ū) > 0. (iii) What are the vectors we R3 such that f(w) = 0?
2. Let ū= (3,1, -7), ã = (1,0,5). (a) Find the vector component of u along a. (b) Find the vector component of ü orthogonal to ä. (c) Find the angle between u and , in degrees.
5 3 1 Let ū = < 2,-3> V = <-2,0 > w = <3,3 > Graph vectors ū, ū, and w in standard position with corresponding terminal points, A, B, and C, respectively. (72 point) What is the length of the altitude of AABC from vertex A? (72 point) -5 -3 -1 -1 0 1 3 5 -3 -5
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=