Answer to Question #110744 in Analytic Geometry for Luk

Question

If \\(a=3i-2j+k\\), \\(b=2i-4j-3k\\) and \\(c=-i+2j+2k\\), find the magnitude of \\(a+b+c\\)

Answer 1

Analytic Geometry

We need to find the magnitude of the sum of given vectors.

Solution:

The given vectors are,

$$\vec a = 3i-2j+k\\ \vec b = 2i-4j-3k\\ \vec c =-i+2j+2k$$

Sum of the vectors $= \vec a + \vec b + \vec c$

$$= 3i-2j+k + 2i-4j-3k + -i+2j+2k$$

$$= 4i - 4 j$$

Magnitude of the given vectors

$$= |\vec a + \vec b + \vec c| = \sqrt {4^2 + (-4)^2} = \sqrt {(16 +16)} = \sqrt {32}$$

$$= 4 \sqrt 2$$

Magnitude of the given vectors =$4 \sqrt 2$