Question

Determine the magnitude and direction of i + j and i - j.

Answer 1

Answer:

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Answer 2

Answer:

$\sqrt{2},\ \sqrt{2}, 45^o,\ -45^o$

Explanation:

Let's consider that

$\overline{A}=i\ +\ j$

and $\overline{B}=\ i\ -\ j$

Since, the given terms are vectors so, we have to apply vector rule to find their magnitude and direction.

$\textrm{Magnitude\ of}\overline{A},\ A=\sqrt{x^2+y^2}\\\\=\sqrt{1^2+1^2}\\\\\ \ \ \ =\sqrt{2}$

$\textrm{Magnitude\ of}\overline{B},\ B=\sqrt{x^2+y^2}\\\\=\sqrt{1^2+(-1)^2}\\\\\ \ \ \ =\sqrt{2}$

$\textrm{Direction\ of}\overline{A}\ =\ tan^{-1}\dfrac{y}{x}\\\\\ \ \ \ =tan^{-1}\dfrac{1}{1}\\\\\ \ \ \ =45^o$

$\textrm{Direction\ of}\overline{B}\ =\ tan^{-1}\dfrac{y}{x}\\\\\ \ \ \ =tan^{-1}\dfrac{-1}{1}\\\\\ \ \ \ =-45^o$

So, the magnitude and direction of vector A is $\sqrt{2}$ and $45^o$ respectively and magnitude and direction of vector B is $\sqrt{2}$ and $-45^o$.