Question

part b
now multiply vector v with the negative scalar value -4 and write the component form of the resulting vector, -4v.

Explanation:

Step1: Recall scalar multiplication of vectors

To multiply a vector \(\mathbf{v} = \langle v_1, v_2
angle\) by a scalar \(k\), we use the rule \(k\mathbf{v}=\langle kv_1, kv_2
angle\). But since the vector \(\mathbf{v}\) is not given in the problem, we assume that maybe there was a prior part (Part A) where \(\mathbf{v}\) was defined. For example, if \(\mathbf{v}=\langle a,b
angle\), then \(-4\mathbf{v}=\langle -4a, -4b
angle\). Wait, but the problem as presented here is incomplete because the vector \(\mathbf{v}\) (its component form) is not provided. However, if we assume a general vector \(\mathbf{v}=\langle v_x, v_y
angle\), then:

Step2: Apply scalar multiplication

Given scalar \(k = -4\) and vector \(\mathbf{v}=\langle v_x, v_y
angle\), the scalar multiplication \(-4\mathbf{v}\) is calculated as:
\(-4\mathbf{v}=\langle -4\times v_x, -4\times v_y
angle=\langle -4v_x, -4v_y
angle\)

But since the problem is missing the component form of \(\mathbf{v}\), we can't compute the numerical component form. However, if we assume that in Part A, say \(\mathbf{v}=\langle 2, 3
angle\) (just an example), then \(-4\mathbf{v}=\langle -4\times2, -4\times3
angle=\langle -8, -12
angle\). But without the actual \(\mathbf{v}\), we can only provide the formula. Wait, maybe the original problem had \(\mathbf{v}\) defined earlier. Since the user's problem is about scalar multiplication of vectors, which is a topic in Mathematics (subfield: Linear Algebra or Algebra).

But as the problem is presented, it's incomplete. However, if we proceed with the general rule:

If \(\mathbf{v}=\langle v_1, v_2
angle\), then \(-4\mathbf{v}=\langle -4v_1, -4v_2
angle\)

Answer:

The problem is incomplete as the component form of vector \(\mathbf{v}\) is not provided. If \(\mathbf{v}=\langle v_1, v_2
angle\), then \(-4\mathbf{v}=\boldsymbol{\langle -4v_1, -4v_2
angle}\). To get a numerical answer, the component form of \(\mathbf{v}\) (from Part A) is needed.