In Exercises 1–6, determine which sets of
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- Section 5-2 : Vector Arithmetic 1. Given ā = 31 -9j and b = -6i +j compute each of the following. (a) 105 (b) 14ã + 205 (c) 8b – 3 2. Find a unit vector that points in the same direction as a = (10,-3,8,-2). 3. Find a unit vector that points in the opposite direction as č = 2i +7j - 5k . 4. Find a vector that points in the opposite direction as ā = (-3,–14,2) with a magnitude of 32. 5. Determine if i = (1,0,-4) and w= (9,3,1) are parallel vectors.arrow_forwardAre the vectors –2 – 8x + 4x2, – 4 – 12x – 20x? and -4 – 14x – 6x? linearly independent? choose If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0 = (-2 – 8x + 4x?)+ (-4 — 12г — 20г?)+ (-4 — 14г — ба?).arrow_forwardIn Exercises 1–6, determine which sets of vectors are orthogonal.arrow_forward
- Part b L Let U₁ = 1 + x + 4x², U₂ = 2x + 5x², U3 = 2 + x + 7x². Determine whether these three vectors are linearly independent or not.arrow_forwardIn Exercises 9–16, find the component form of the vector.arrow_forward6. Show that the vectors (1,1,0), (1, 0, 1), and (0, 1, 1) generate F³.arrow_forward
- Draw the result of -u+2u-w as a single vector.arrow_forwardThe following question is from linear algebra first year: Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step. Can we get integers as answers?arrow_forwardFind a vector orthogonal to both 7 -10 and w -10 -10 -4 7arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage