Question

Given two vectors A=6i + 3j - k and B = 4i -5j + 8k , find the magnitude of the vector 2A - 3B.

Answer 1

$A=6\hat{i}+3\hat{j}-\hat{k}\\B=4\hat{i}-5\hat{j}+8\hat{k}$

$$2A-3B=2(6\hat{i}+3\hat{j}-\hat{k})-3(4\hat{i}-5\hat{j}+8\hat{k})$$

$2A-3B=0\hat{i}+21\hat{j}-26\hat{k}$

Magnitude of vector

$$|2A-3B|=\sqrt{0^2+21^2+(-26)^2}=\sqrt{1117}=33.42$$