Question

Let u=(-1,3), v=( 2,4) , and w= (2,-5) . Find the component forms of the following vectors. -4 \mathrm{w}

Answer 1

Applying the rules of addition and scalar multiplication of vectors, –4w = (–8, 20) and –4u + w = (6, –7)

In the 2D coordinate system, vectors can be split into x-component and y-component.

we can write, for example, a vector r = (2,–6), which means:

x-component = 2

y-component = –6

• Addition / subtraction of vectors: Just add or subtract the corresponding components.
  For example: r = (2,–6) and s = (-2,3)
  Then,
  r + s = (2,–6) +  (-2,3) = (2–2, –6+3) = (0,–3)
• Scalar multiplication: Multiply each component by the given scalar.
  For example: r = (2,–6)
  Then,
  6r = 6.(2,–6) = (6 . 2, 6 . (–6)) = (12,–36)

In the given problem:

u = (-1,3), v = ( 2,4) , and w = (2,-5)

Then,

–4w =  –4(2, –5)

       = (–4 . 2, –4. (–5)) = (–8, 20)

–4u + w =  –4(-1,3) + (2, –5)

             = (–4.(–1), –4 . 3) +(2, –5)

             =(4, –12) + (2, –5)

             = (4+2, –12–(–5)) = (6, –7)

Learn more about vector addition and scalar multiplication here:

brainly.com/question/13592198

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