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express the magniyude of vector a x b in terms of scalar products.

|a \times b| = |a| |b| \sin (θ) - - - (1) (θ i s t h e a n g l e b e t w e e n a a n d b) a . b = |a| |b| \cos (θ) - - - (2) \cos (θ) = \frac{a . b}{|a| |b|} \sin (θ) = \sqrt{1 - \cos^{2} (θ)} = \sqrt{1 - {(\frac{a . b}{|a| |b|})}^{2}} p u t t i n g v a l u e o f \sin (θ) i n e q u a t i o n (1) |a \times b| = |a| |b| \sqrt{1 - {(\frac{a . b}{|a| |b|})}^{2}} \frac{|a \times b|}{|a| |b|} = \sqrt{1 - {(\frac{a . b}{|a| |b|})}^{2}} s q u a r i n g b o t h s i d e s {(\frac{|a \times b|}{|a| |b|})}^{2} = \frac{{(|a| |b|)}^{2} - {(a . b)}^{2}}{{(|a| |b|)}^{2}} |a \times b| = \sqrt{{{(|a| |b|)}^{2} - (a . b)}^{2}}

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