Answer:
Magnitude of A=5
Magnitude of B=5.39
Explanation:
The magnitude of Vectors in Rectangular Form
Given a vector v in its rectangular form:
[tex]\mathbf{v}=x\hat i+y\hat j[/tex]
The magnitude of v is:
[tex]\mid\mid\mathbf{v}\mid \mid=\sqrt{x^2+y^2}[/tex]
We are given the vectors
[tex]\mathbf{A}=4\hat i+3\hat j[/tex]
[tex]\mathbf{B}=5\hat i-2\hat j[/tex]
Their magnitudes are:
[tex]\mid\mid\mathbf{A}\mid \mid=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}[/tex]
[tex]\mid\mid\mathbf{A}\mid \mid=5[/tex]
[tex]\mid\mid\mathbf{B}\mid \mid=\sqrt{5^2+(-2)^2}=\sqrt{25+4}=\sqrt{29}[/tex]
[tex]\mid\mid\mathbf{B}\mid \mid=\sqrt{29}=5.39[/tex]
