# Find the magnitude and direction of the vectors i + j and i - j.

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Find the magnitude and direction of the vectors $\hat i\,+\,\hat j$ and $\hat i\,-\,\hat j$.

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(i) Magnitude of vectors $\vec i+\vec j$

= | $\hat i +\hat j$|

= $\sqrt{1^2+1^2}=\sqrt2$

tan θ = $\frac{|\hat j|}{|\hat i|}=\frac{1}{1}$ = 1

or θ = $tan^1\, 1$ = 45º with X-axis

(ii) Magnitude of vectors $\hat i-\hat j$

= | $\hat i-\hat j$|

= | $\sqrt{1^2+(-1)^2}$ | = $\sqrt2$

tan θ = $\frac{|-\hat j|}{|\hat i|}=\frac{-1}{1}$ = −1

θ = tan-1(−1)

= −45 with X-axis