I was doing vector algebra and in a solution to a problem where the angle between the vectors was to be found, i got \(cos \theta\) = -10 / 102^1/2,
so can i write \(theta\)=cos^-1 (10/102^1/2)=cos^-1 ( -10/102^1/2 ). Please explain the former one.

Vectors have two components, direction and magnitude (similar to length). When you say \(\cos^{-1} (10/\sqrt{102}\)) you are saying that the \(\cos \theta= \frac{-10}{\sqrt{102}}=\frac{10}{\sqrt{102}}\). This is obviously incorrect since cosine is the trig function dealing with x values and you have changed the x value from positive to negative.

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TopNewestVectors have two components, direction and magnitude (similar to length). When you say \(\cos^{-1} (10/\sqrt{102}\)) you are saying that the \(\cos \theta= \frac{-10}{\sqrt{102}}=\frac{10}{\sqrt{102}}\). This is obviously incorrect since cosine is the trig function dealing with x values and you have changed the x value from positive to negative.

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