Suppose length of vector v= 3 and (vector v) dot product (vector u) = -18. What can you say about length of vector u?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluuate the dot product of the given vectors `bar u` and` bar v` , such that:

`bar u*bar v = |bar u|*|bar v|*cos theta`

theta represents the angle between the vectors `bar u,bar v`

The problem provides the magnitude of the vector `bar v` , `|bar v| = 3` and the dot product of the given vectors `bar u` and `bar v` , such that:

`-18 = 3*|bar u|*cos theta => |bar u|*cos theta = -18/3`

`|bar u|*cos theta = -6 => |bar u| = -6/(cos theta)`

Since the length of bar u needs to be a positive value, hence, `-1 < cos theta < 0` .

Hence, evaluating the length of the vector bar u yields that `|bar u| >= 6` .