Determine which pairs 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_forwardIn Exercises 25–30, express each vector as a product of its length and direction. 25. 2i + j - 2k 26. 9i – 2j + 6k 27. 5k 28. i + k 29. V6 30. V3 -i V6 V3 V3arrow_forward1. Find the sum of the vectors (3,-1) and (-1,5) and illustrate geometrically.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 1–6, determine which sets of vectors are orthogonal.arrow_forwardIn Exercises 25–30, express each vector as a product of its length and direction. 25. 2i + j - 2k 26. 9i – 2j + 6k 3 4 27. 5k 28. i + k 5 j i 30. V3 k 29. i V6 V6 k V6 V3 V3arrow_forward
- 2. Write 3 as a linear combination of the vectors +arrow_forward1. Let x = i +4j + 2k and y = i-3j - k. In this question, write all vectors in i, j, k notation. (a) ( Find |x||. (b) M Find 2x + 3y. (c) Find x. y. (d) Find x × y. Answer: Answer: Answer:arrow_forward4  write the given vector in terms of I and J. u={-8, 10} u=???arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage