Question

Vector u = <11, 12>, v = <-16, 6>, and w = <4, -5>. Match each vector operation with its resultant vector expressed as a linear combination of the unit vectors i and j.

Answer 1

3u - 2v + w gives the resultant vector as; <49, 19>

8u - 6v gives the resultant vector as; <184, 60>

7v - 4w gives the resultant vector as; <61, 104>

u - 5w gives the resultant vector as; <-9, 37>

How to find the resultant of vectors?

We are given the vectors;

u = 11i + 12j

v = -16i + 6j

w = 4i - 5j

1) 3u - 2v + w gives the resultant vector as;

3(11i + 12j) - 2(-16i + 6j) + 4i - 5j

⇒ 33i + 36j + 32i - 12j + 4i - 5j

⇒ 49i + 19j

⇒ <49, 19>

2) 8u - 6v gives the resultant vector as;

8(11i + 12j) - 6(-16i + 6j)

⇒ 88i + 96j + 96i - 36j

⇒ 184i + 60j

3) 7v - 4w gives the resultant vector as;

7(11i + 12j) - 4(4i - 5j)

⇒ 77i + 84j - 16i + 20j

⇒ 61i + 104j

4) u - 5w gives the resultant vector as;

11i + 12j - 5(4i - 5j)

11i + 12j - 20i + 25j

-9i + 37j

Read more about Resultant Vectors at; brainly.com/question/110151

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