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Two vectors
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- For what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?arrow_forwardFind the x− and y− components of the vectors A~, B~ , C~ , and D~ . TakeA = 10.0, B = 7.00, C = 10.0, and D = 9.00, and take the angles of thesevectors with respect to the +x axis to be 63◦ 161.6◦, 156◦, and 307◦,respectivelyarrow_forwardFor any arbitrary vectors u, v and w, prove thatarrow_forward
- Show that the vectors a = 2i+4j−8k, b = 3i−j+3k and c = −5i+11j−25k are coplanar.arrow_forwardFind 2 unit vectors orthogonal to both u = <4,-2,3> and v = <0,3,7>.arrow_forwardVectors A ⃗ and B ⃗ are two orthogonal vectors in the xy-plane and they have identical magnitudes. If A ⃗ = 3.0i ^ + 4.0j ^ , find B ⃗ .arrow_forward
- For the vectors A=8.94i +6.93j-17.9k, B=7.67i-6.06j+10.2k, and C=6.25i-3.34j-9.61k, find C(A-B).arrow_forwardIf A = 4i − 3k and B = −2i + 2j − k, find the scalar projection of A on B, the scalar projection of B on A, and the cosine of the angle between A and B.arrow_forwardLet vector A point from the origin into the second quadrant of the xy plane and vector B point from the origin into the fourth quadrant. The vector B −A must be in which quadrant?arrow_forward
- Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there exists some vectorin V that can be written as a nontrivial linear combinationof other vectors in V.arrow_forwardConsider the three displacement vectors = (−2î− 3ĵ) m, = (4î − 5ĵ) m, and = (−6î + 5ĵ) m. Use the component method to determine the following. (Take the +x direction to be to the right.)arrow_forwardConsider the two vectors, A=17x+11.5y, B=4.5x-3.5y. What is the angle of the vector A-B, measured counterclockwise in degrees from the positive x-axis?arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning