(6 marks) Suppose that u, v and w are vectors in R3, and that u. (v x w) = 3. Determine (a) u (w xv) (b) u. (w xw) (c) (2u x v). w
3. (6 marks) Suppose that u, v and w are vectors in R3, and that u. (v x w) = 3. Determine (a) u (w x v) (b) u: (w X w) (c) (2u x v). w
(6 marks) Suppose that u, v and w are vectors in R 3 , and that u · (v × w) = 3. Determine 3. (6 marks) Suppose that u, v and w are vectors in R3, and that u. (vx w) = 3. Determine (a) u (w xv) (b) u (w xw) (c) (2u xv).w
Find 2u, -3v, u + v, and 3u - 4v for the given vectors u and v. (Simplify your answers completely.) u = i, v= -4j 2u = -3v = u + V = 3u - 4 = 17. [-12.94 Points) DETAILS SPRECALC75.3.024. Find the amplitude and period of the function. y = -5 sin(6x) amplitude period Sketch the graph of the function. AA Am Type here to search A
13) For the vectors u = (7,3) and w=(-4,6) find all of the following a) 2u – 3w b) will c) Wow d) Explain how you know if two vectors are orthogonal to each other.
1.8.18 Question Help The figure shows vectors u. v, and w, along with the images Tu) and (v) under the action of a linear transformation T R2-R2 Copy this figure carefully and drew the image (W) as accurately as possible T Which figure displays the correct image of (w)? OA OB Ос. Q TH Tu TUT TV TW) TV TV
LD "Law fCosines" comes from(U-u,): (u-w) u . u-2u . to +to. Cosine Law liu-w12-11 , 12-211Uİl lltv11 cose+11 ll2. es" comes from (v -w(-2vw Draw a triangle with sides u and w and u-u, which of the angles is 82
Given the following vectors u and v, find a vector w in R4 so that {u, v, w} is linearly independent and a non- zero vector z in R4 so that {u, v, z} is linearly dependent: 1-3 8 -8 -2 u = V= 5 -4 10 0 w=0 1- z=0 0
Problem 1. The figure below shows the vectors u, v, and w, along with the images T(u) and T(v) to the right. Copy this figure, and draw onto it the image T(w) as accurately as possible. (Hint: First try writing w as a linear combination of u and v.) TV (u) Problem 2. Let u = | and v Suppose T : R2 + R2 is a linear transformation with 6 1 3) Tu = T(u) = -3 and T(v)...
Use the given vectors to find u. (v + w). u = -21 - 9j, v= - 21 + 8j, w = -5i + 5j A. - 35 B. - 103 C. -68 OD. 37 Find the unit vector that has the same direction as the vector v. v = 24i + 10j The unit vector that has the same direction as the vector v is . (Simplify your answer, including any radicals. Use integers or fractions for any nume