vactors vec u vec v are colinear what is a? vec u=ai+2j vec v=2i+(a-3)j

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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.`

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