Question

Vector A + B = (3, -1) and vector A - B = (2, 1). What is the magnitude of A?

I keep getting = 2.69258... but my professor posted that the solution is 2.5 please help me

Answer 1

Given $\vec{A}+\vec{B}=3i -j$ -------------------(1)

and $\vec{A}-\vec{B}=2i +j$ ------------------------(2)

Add (1) and (2)

$(\vec{A}+\vec{B})+(\vec{A}-\vec{B})=(3i-j)+(2i +j)$

$2\vec{A}=3i-j+2i +j$

$2\vec{A}=5i$

$\vec{A}=2.5i$

$A =\sqrt{2.5^{2}}$

ANSWER: ${\color{Red} A =2.5}$

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