Mathematics: Given that u=(-3,4) and vector v has an initial point of (7,0) and a terminal point of (-5,2), find 2v-3u and express your answer as a linear combination of i and j

Given that u=(-3,4) and vector v has an initial point

nicollexo21

27.01.2022

The linear combination $2\cdot \vec v -3\cdot \vec u$ is equal to $\vec r = -42\cdot i + 14\cdot j$

The resultant vector is a linear combination of the two vectors described in statement, which is calculated as follows:

$\vec r = -3\cdot (-3,4) + 2\cdot (-5-7,2-0)$

$\vec r = (9, -12) + (-24, 4)$

$\vec r = (-15, -8)$

$\vec r = -15\,\hat{i}-8\,\hat{j}$

The answer as a linear combination of $\vec u$ and $\vec v$ is $\vec r = -15\,\hat{i}-8\,\hat{j}$ .

We kindly invite to check this question on linear combinations: link

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