Question

Given two vectors A = -2.00i + 4.00 j + 4.00 k and B = 4.00 i + 1.00 j - 3.00A; do the following. Find the magnitude of the vector A. Find the magnitude of the vector B. Write an expression for the vector difference A- B Enter your answers numerically separated by commas. Find the magnitude of the vector difference A - B. Is this the same as the magnitude of B - A?

Answer 1

$\large \overset{}{\rightarrow}A=-2.0i+4.0j+4.0k$

$\large \overset{}{\rightarrow}B=4.0i+1.0j-3.0k$

Part 1

$\large I\overset{}{\rightarrow}AI=\sqrt{2^2+4^2+4^2}=6unit$

Part 2

$\large I\overset{}{\rightarrow}BI=\sqrt{4^2+1^2+3^2}=5.1unit$

Part 3

$\large \overset{}{\rightarrow}A-\overset{}{\rightarrow}B=(-2.0i+4.0j+4.0k)-(4.0i+1.0j-3.0k)$

$\large \overset{}{\rightarrow}A-\overset{}{\rightarrow}B=(-6.0i+3.0j+7.0k)$

$\large x=-6,y=3,z=7$

Part D

IA-Bl = V62 + 32 + 72 = 9.695 unit

$\large \overset{}{\rightarrow}B-\overset{}{\rightarrow}A=(4.0i+1.0j-3.0k)-(-2.0i+4.0j+4.0k)$

B _ A = (6.01-3.0jー7.0k)

Part E

$\large I\overset{}{\rightarrow}B-\overset{}{\rightarrow}AI=\sqrt{6^2+3^2+7^2}=9.695unit$

Yes it is same