Question

given the vectors m = ⟨2, 1⟩ and n = ⟨-3, -8⟩, find -2m and m - n. write your answers in component form. -2m = ⟨□,□⟩ m - n = ⟨□,□⟩

Explanation:

Step1: Calculate \(-2m\)

For a vector \(m=\langle a,b
angle\), \(km = \langle ka,kb
angle\). Here \(m=\langle2,1
angle\) and \(k=-2\).
\(-2m=\langle-2\times2,-2\times1
angle\)

Step2: Calculate \(m - n\)

For vectors \(m=\langle a_1,b_1
angle\) and \(n=\langle a_2,b_2
angle\), \(m - n=\langle a_1 - a_2,b_1 - b_2
angle\). Here \(a_1 = 2\), \(b_1=1\), \(a_2=-3\), \(b_2 = -8\).
\(m - n=\langle2-(-3),1-(-8)
angle=\langle2 + 3,1+8
angle\)

Answer:

\(-2m=\langle-4,-2
angle\)
\(m - n=\langle5,9
angle\)