Find the magnitude of the vector described below.
Initial point: $( 5,6 , - 4 )$
Terminal point: $( - 4,2,7 )$
A) 2
B) 36
C) $2 \sqrt { 6 }$
D) $2 \sqrt { 218 }$
E) $\sqrt { 218 }$

Question

Quizplus · Accepted Answer

The magnitude of a vector from point $A(x_1, y_1, z_1)$ to point $B(x_2, y_2, z_2)$ is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$. Substituting the given points, we get $\sqrt{(-4 - 5)^2 + (2 - 6)^2 + (7 - (-4))^2} = \sqrt{(-9)^2 + (-4)^2 + (11)^2} = \sqrt{81 + 16 + 121} = \sqrt{218}$.

Find the Magnitude of the Vector Described Below (5,6,−4)( 5,6 , - 4 )(5,6,−4)

Find the Magnitude of the Vector Described Below $( 5,6 , - 4 )$