What is the magnitude and direction for this vector?  Write vector (1,4) in terms of o(arrow on top) and a(arrow on top) where o= (1,3) and v=(3,0). Finally, What is the magnitude and direction...

What is the magnitude and direction for this vector?

 

Write vector (1,4) in terms of o(arrow on top) and a(arrow on top) where o= (1,3) and v=(3,0).

Finally, What is the magnitude and direction for this vector?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You may get the vector `bar u = lt1,4gt`  only if you add the third vector `bar w = lt-3, 1gt`  such that:

`bar u = bar o + bar v + bar w`

`bar u = lt1,3gt + lt3,0gt + lt-3, 1gt`

You need to add the corresponding components to get the resulting vector bar u such that:

`bar u = lt1+3-3 , 3+0+1gt`

`bar u = lt1,4gt`

The magnitude of the vector bar u is the length of this vector and you may find it using the formula:

`|bar u| = sqrt(1^2 + 4^2)`

`|bar u| = sqrt 17`

The direction of the vector bar u is the opposite direction to the vector `bar u' = lt-1,-4gt.`

Hence, evaluating the magnitude of the vector bar u yields `|bar u| = sqrt 17 ` and the direction of bar u is opposite to direction of `bar u' = lt-1,-4gt.`

Sources:

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