Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B x A). C, where the vectors A, B, and C are not same plane. ii) in triple cross of vectors (A x B) x C = Cx (B x A). iii) A is 2 x 2 unit matrix, B inverse of matrix A then A = B. iv) in complex number z³. (z)² = |z|².z

Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B x A). C, where the vectors A, B, and C are not same plane. ii) in triple cross of vectors (A x B) x C = Cx (B x A). iii) A is 2 x 2 unit matrix, B inverse of matrix A then A = B. iv) in complex number z³. (z)² = |z|².z

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 11E

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We mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to the Irish mathematician William Rowan Hamilton. Hamilton considered his greatest achievement to be the discovery of qualernions, which he (incorrectly) predicted would revolutionize physics. Research the subject of quaternions. What are they? Why did quaternions fail to be as useful for physics as Hamilton predicted? How are quaternions useful, instead, for 3.D computer graphics? Write a paragraph or two about your findings.
Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.

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