The vector A^vector has x, y, and z components of -4.00, 6.00, and 3.00 units, r
ID: 1655083 • Letter: T
Question
The vector A^vector has x, y, and z components of -4.00, 6.00, and 3.00 units, respectively. (a) Write a vector expression for A^vector in unit-vector notation. (_______ i^Hat + ______ j^Hat + ________ k^Hat) units (b) Obtain a unit-vector expression for a vector B^vector one fourth the length of A^Hat pointing in the same direction as A^Hat. (_______ i^Hat + ______ j^Hat + ________ k^Hat) units (c) Obtain a unit-vector expression for a vector C^Hat three times the length of A^Hat pointing in the direction opposite the direction of A^Hat. (_______ i^Hat + ______ j^Hat + ________ k^Hat) units If A^vector = (7.00 i^Hat -9.00 j^Hat) units, B^Hat = (-9.00 i^Hat + 4.00 j^Hat) units, and C^vector = (27.0 i^Hat + 19.0 j^Hat) units, determine a and b such that a A^vector + b B^vector + C^vector = 0. a = _______ units b = _______ unitsExplanation / Answer
a) -4i + 6j + 3k
b) Magnitude of A = sqrt(4^2+6^2+3^2) = 7.81
unit vector of B is same as A as direction is same
so unit vector= (-4i+6j+3k)/7.81
= -0.51 i + 0.77j + 0.38k
c) this unit vector is opposite of A,
= 0.51 i - 0.77j - 0.38k
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