Question

part b
now multiply vector v with the negative scalar value -4 and write the component form of the resulting vector, -4v.
-4v=(-4v₁,-4v₂)
space used(includes formatting): 44 / 30000
submitted!
show sample answer
part c
find the direction and magnitude of vector -4v.

Explanation:

Step1: Recall Scalar Multiplication Rule

For a vector \(\mathbf{v}=(v_1, v_2)\), scalar multiplication by \(k\) is \(k\mathbf{v}=(kv_1, kv_2)\). Here \(k = - 4\), so \(-4\mathbf{v}=(-4v_1, - 4v_2)\).

Step2: Apply to Find Component Form

Using the scalar - vector multiplication formula, if \(\mathbf{v}=(v_1,v_2)\), then multiplying each component by \(-4\) gives the component form of \(-4\mathbf{v}\) as \((-4v_1,-4v_2)\).

Answer:

\(-4\mathbf{v}=(-4v_1, - 4v_2)\) (assuming \(\mathbf{v}=(v_1,v_2)\) in component form)