Find the component form and the magnitude of the vector v. Initial Point
Terminal Point
(1,3)
(-8,-9)
A) $\mathbf { v } = \langle 1 , - 8 \rangle ; \| \mathbf { v } \| = 15$
B) $\mathbf { v } = \langle - 9 , - 12 \rangle ; \| \mathbf { v } \| = 8$
C)? $\mathbf { v } = \langle - 9 , - 12 \rangle ; \| \mathbf { v } \| = 15$
D)? $\mathbf { v } = \langle - 8 , - 9 \rangle ; \| \mathbf { v } \| = 12$
E)? $\mathbf { v } = \langle 1 , - 8 \rangle ; \| \mathbf { v } \| = 8$

Question

Quizplus · Accepted Answer

The component form of a vector is found by subtracting the coordinates of the initial point from the coordinates of the terminal point, giving $\mathbf{v} = (-8 - 1, -9 - 3) = (-9, -12)$. The magnitude is calculated using the Pythagorean theorem, $\| \mathbf{v} \| = \sqrt{(-9)^2 + (-12)^2} = \sqrt{81 + 144} = \sqrt{225} = 15$.

Find the Component Form and the Magnitude of the Vector v=⟨1,−8⟩;∥v∥=15\mathbf { v } = \langle 1 , - 8 \rangle ; \| \mathbf { v } \| = 15v=⟨1,−8⟩;∥v∥=15

Find the Component Form and the Magnitude of the Vector $\mathbf { v } = \langle 1 , - 8 \rangle ; \| \mathbf { v } \| = 15$