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- 2. If , and the vector is drawn with its tail at the point, find the coordinates of the point at the head of .arrow_forwardEach problem below refers to a vector V with magnitude ) V ) that forms an angle u withthe positive xaxis. In each case, give the magnitudes of the horizontal and vertical vectorcomponents of V, namely Vx and Vy, respectively. ) V ) = 425 , u = 36 degree 10 degreearrow_forwardIn Problems 45–50, find the unit vector in the same direction as v.45. v = 5i 46. v = - 3j 47. v = 3i - 6j - 2k 48. v = - 6i + 12j + 4k 49. v = i + j + k 50. v = 2i - j + karrow_forward
- In Problems 40–45, use the vectors v = 3i + j - 2k and w = - 3i + 2j - k to find each expression. 40. 4v - 3w 41. || v - w || 42. || v || - || w || 43. v * w 44. v . (v * w) 45. Find a unit vector orthogonal to both v and w.arrow_forwardIn Problem ,find the unit vector in the same direction as v. v = 5iarrow_forwardQuestions (a) and (b) in this problem refer to the vectors u = 1 −2 2 and y = −2 1 −1(a) Find the orthogonal projection of y onto the line through u.(b) Write y as the sum of two vectors, where the first is in Span{u} and the second is orthogonalto u.arrow_forward
- Each problem below refers to a vector V with magnitude ) V ) that forms an angle u withthe positive xaxis. In each case, give the magnitudes of the horizontal and vertical vectorcomponents of V, namely Vx and Vy, respectively. ) V ) = 17.6 , u = 72.6 degreearrow_forwardAssignment 4 Problem 5: Determine if the pairs of vectors below are "parallel", "orthogonal", or "neither".arrow_forwardgiven the vector, PQ, whose initial point is P(-2,-5) and whose terminal point is Q(3,4) the position vector, v, which is equal to the vector, PQ, is given byarrow_forward
- what if it was the same vector, but 5y^2j?arrow_forwardThe problem below refers to a vector V with magnitude |V| that forms an angle θ with the positive x-axis. In this case, give the magnitudes of the horizontal and vertical vector components of V, namely Vx and Vy, respectively. (Round each answer to the nearest whole number.) |V| = 52, θ = 0°arrow_forwardThe problem below refers to a vector V with magnitude |V| that forms an angle θ with the positive x-axis. In this case, give the magnitudes of the horizontal and vertical vector components of V, namely Vx and Vy, respectively. (Round each answer to the nearest whole number.)arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning