Question

If A = 3i+2j : B=i-2j+3k , find the magnitudes of A + B and A- 3.​

Answer 1

Given:

$\overrightarrow{A}=3\hat{i}+2\hat{j} \; ;\; \overrightarrow{B}=\hat{i}-2\hat{j}+3\hat{k}$

To find:

$Magnitudes \;of\;A+B \; ; \;A-B.$

Solution:

A + B :-

$3\hat{i}+2\hat{j} + \hat{i}-2\hat{j}+3\hat{k}$

$4\hat{i}+3\hat{k}$

• √(4)² + (3)²
• √16 + 9
• √25

∴ 5 is the magnitude of A + B.

A - B :-

$3\hat{i}+2\hat{j}- (\hat{i}-2\hat{j}+3\hat{k})$

$2\hat{i}+4\hat{j}-3\hat{k}$

• √(2)² + (4)² + (-3)²
• √4 + 16 + 9
• √29
• 5.385 ≈ 5.4

∴ 5.4 is the magnitude of A - B.