Question

Let a=(1,2,3), b=(-5,3,-2), c=(2,-4,1) be three points in R³. Find |2b - a + 3c|.

Answer 1

$$\vec a=(1,2,3)$$

$$\vec b=(-5,3,-2)$$

$$\vec c=(2,-4,1)$$

$$2\vec b-\vec a+3\vec c=2(-5,3,-2)-(1,2,3)+3(2,-4,1)$$

$$=(-10-1+6,6-2-12,-4-3+3)$$

$$=(-5,-8, -4)$$

$$|2\vec b-\vec a+3\vec c|=\sqrt{(-5)^2+(-8)^2+(-4)^2}=\sqrt{105}$$