Question

question
type the correct answer in each box. round the vector’s magnitude to the nearest hundredth.
vector v has its initial point at (11, -4) and its terminal point at (4, -5). write the vector in component form and find its magnitude.

v = <box, box>, and ||v|| ≈ box units.

Explanation:

Step1: Find component form

To find the component form of a vector with initial point \((x_1, y_1)\) and terminal point \((x_2, y_2)\), we use the formula \(\mathbf{v}=\langle x_2 - x_1, y_2 - y_1
angle\). Here, \(x_1 = 11\), \(y_1=-4\), \(x_2 = 4\), \(y_2=-5\). So, \(x_2 - x_1=4 - 11=-7\) and \(y_2 - y_1=-5-(-4)=-5 + 4=-1\). Thus, \(\mathbf{v}=\langle - 7,-1
angle\).

Step2: Find magnitude

The magnitude of a vector \(\mathbf{v}=\langle a,b
angle\) is given by \(\|\mathbf{v}\|=\sqrt{a^{2}+b^{2}}\). Substituting \(a = - 7\) and \(b=-1\), we get \(\|\mathbf{v}\|=\sqrt{(-7)^{2}+(-1)^{2}}=\sqrt{49 + 1}=\sqrt{50}\approx7.07\) (rounded to the nearest hundredth).

Answer:

\(\mathbf{v}=\langle -7,-1
angle\), and \(\|\mathbf{v}\|\approx7.07\) units.