Concept explainers
Finding a Point of IntersectionIn Exercises 33–36, determine whether the lines intersect, and if so, find the point of intersection and the angle between the lines.
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Multivariable Calculus
- Plot the points in same three-dimensional coordinate system and determine whether u and v are orthogonal, parallel, or neither u = (-4,3, –6), v = = (16, –12,24)arrow_forwardIn Exercises 25–30, express each vector as a product of its length and direction. 2i + j – 2karrow_forwardWhat are the coordinates of M?arrow_forward
- Use vectors to decide whether the triangle with vertices P(3, -1, -4), Q(4, 2, -6), and R(8, 0, -7) is right-angled. O Yes, it is right-angled. O No, it is not right-angled.arrow_forwardFinding the Component Form of aVector In Exercises 65–70, find thecomponent form of v given its magnitude andthe angle it makes with the positive x-axis.Then sketch v.Magnitude Angle65. ,v, = 3 θ = 0°66. ,v, = 4√3 θ = 90°67. ,v, = 72 θ = 150°68. ,v, = 2√3 θ = 45°69. ,v, = 3 v in the direction 3i + 4j70. ,v, = 2 v in the direction i + 3jarrow_forwardSketch the lines in Exercises 45–48 and find Cartesian equations for them. Зп 45. r cos (0 = V2 46. r cos (0 + 47. r cos (0 - =) rem (0 + 3) = 2 3.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage