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U=(3, 2) v=(4,-3) w=(-2, 5) find u-v+w, 2u+v-3w, 0. 5(u+2v+w)

1 Answer

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To find the results of the given vector operations, we can simply add or subtract the corresponding components of the vectors involved. Here are the calculations:

u - v + w:

(3, 2) - (4, -3) + (-2, 5)

= (3 - 4 - 2, 2 - (-3) + 5)

= (-3, 10)

2u + v - 3w:

2(3, 2) + (4, -3) - 3(-2, 5)

= (6, 4) + (4, -3) - (-6, 15)

= (6 + 4 + 6, 4 - 3 - 15)

= (16, -14)

0.5(u + 2v + w):

0.5[(3, 2) + 2(4, -3) + (-2, 5)]

= 0.5[(3, 2) + (8, -6) + (-2, 5)]

= 0.5[(3 + 8 - 2, 2 - 6 + 5)]

= 0.5[(9, 1)]

= (4.5, 0.5)

So, the results of the given vector operations are:

u - v + w = (-3, 10)

2u + v - 3w = (16, -14)

0.5(u + 2v + w) = (4.5, 0.5)

User Mdominick
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