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vactors vec u vec v are colinear what is a? vec u=ai+2j vec v=2i+(a-3)j
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You should remember that two vectors are collinear if one vector is the multiple of the other such that:
`bar u = k*bar v => (bar u)/(bar v) = k`
Hence, reasoning by analogy, you need to consider the following fractions equal such that:
`a/2 = 2/(a - 3)=> a(a-3) = 4 => a^2- 3a - 4 = 0`
You need to use quadratic formula such that:
`a_(1,2) = (3+-sqrt(9 + 16))/2 => a_(1,2) = (3+-sqrt25)/2`
`a_(1,2) = (3+-5)/2 => a_1 = 4 ; a_2 = -1`
Hence, evaluating the values of a under the given condition of collinearity yields `a_1 = 4 ; a_2 = -1.`
Posted by sciencesolve on August 21, 2012 at 12:28 PM (Answer #1)
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