1Dot 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
