Find the magnitude and angle with +x-axis of a vector -i + j.

1.	Find the magnitude and angle with +x-axis of a vector -i + j.
Answer» Given vector = \(-\hat i + \hat j\) Magnitude will be = \(\sqrt{1 + 1}\) = \(\sqrt 2\) Angle \(cos \theta = \frac {i.(-\hat i + \hat j)}{\|i\|\|-i + j\|}\) \(= \frac{-1}{1 \times \sqrt 2}\) \(cos \theta = \frac {-1}{\sqrt 2}\) \(cos \theta = cos 135° \) \(\theta = 135° \)

Answer»

Given vector = \(-\hat i + \hat j\)

Magnitude will be = \(\sqrt{1 + 1}\) = \(\sqrt 2\)

Angle

\(cos \theta = \frac {i.(-\hat i + \hat j)}{|i||-i + j|}\)

\(= \frac{-1}{1 \times \sqrt 2}\)

\(cos \theta = \frac {-1}{\sqrt 2}\)

\(cos \theta = cos 135° \)

\(\theta = 135° \)

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Find the magnitude and angle with +x-axis of a vector -i + j.

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