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

Question

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

Answer 1

(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