For the vectors u = <-3, 4> & v=<4,5> , find 3u+2v & u-v

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have u = < -3, 4> and v = < 4, 5>

=> u = -3i + 4j and v = 4i + 5j

3u + 2v

=> 3*(-3i + 4j) + 2*(4i + 5j)

=> -9i + 12j + 8i +10j

=> -i + 22j

u - v

=> -3i + 4j - 4i - 5j

=> -7i - j

The required values are : 3u + 2v = -i + 22j and u - v = -7i - j

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

u = -3i + 4j

v = 4i + 5j

3u + 2v = 3(-3i + 4j) + 2(4i + 5j)

We'll open the brackets:

3u + 2v = -9i + 12j + 8i + 10j

We'll combine like terms:

3u + 2v = -i + 22j

We'll calculate u - v:

u - v = -3i + 4j - 4i - 5j

We'll combine like terms:

u - v = -7i - j

The results for the requested vectorial expresisons are: 3u + 2v = -i + 22j and u - v = -7i - j.

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