Question

Given two vectors A=4i^+3j^ and vector B=5i^-2j^.find the magnitude of each vector

Answer 1

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:

$\mathbf{v}=x\hat i+y\hat j$

The magnitude of v is:

$\mid\mid\mathbf{v}\mid \mid=\sqrt{x^2+y^2}$

We are given the vectors

$\mathbf{A}=4\hat i+3\hat j$

$\mathbf{B}=5\hat i-2\hat j$

Their magnitudes are:

$\mid\mid\mathbf{A}\mid \mid=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}$

$\mid\mid\mathbf{A}\mid \mid=5$

$\mid\mid\mathbf{B}\mid \mid=\sqrt{5^2+(-2)^2}=\sqrt{25+4}=\sqrt{29}$

$\mid\mid\mathbf{B}\mid \mid=\sqrt{29}=5.39$