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# Dot product of vectors

B.Sudhakar
31/12/2016 0 1

Dot product of two vectors gives back a number ( scalar )

If "a and b" are two vectors, then their cross product ( a • b ) = | a |  | b | cos θ

| a | & | b | are the magnitude of vectors "a and b" and cos θ is the angle between two vectors.

Ex: a= 2i + j + 4k,.    b= 3i + 5j - k find ( a • b )

( a • b ) = ( 2 x 3 +1 x 5 + 4 x -1 )= 6 + 5 + (-4 ) = ( 11 - 4 )= 7

Now angle between vectors "a & b"

θ = arc cos (a • b )/| a | | b |      | a | = √2² + 1² + 4² = √21,  | b |= √3² + 5² + (-1² )= √35

θ= arc cos 7/( √21 + √ 35 ) = arc cos 7 /( 4.58 + 5.92 ) = arc cos ( 7/ 10.5 )

= arc cos 0.666

θ= 48.2º

If dot product of two vectors is zero, then two vectors are perpendicular to each other since   cos 90 = 0

0 Dislike

K

Karthik | 02/01/2017

Neatly explained. Wish to see more such lessons in future.

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