Cross Product is given by,Cross Product Formula is given by,
Cross product formula is used to determine the cross product or angle between any two vectors based on the given problem.
Solved Examples
Question 1:Calculate the cross products of vectors a = <3, 4, 7> and b = <4, 9, 2>.
Solution:
The cross product is given by
a
a
a
a
Question 2:
Find the angle between two vector a and b, where a =<-4, 3, 0> and b =<2, 0, 0>
Solution:
We know that, the formula to find the angle between two vectors is
Sin θ = a × b / |a| |b|
Therefore, θ = sin-1[a × b / |a| |b|]
Now, we have to find the cross product of two vectors and b:
= i (0) -j(0) +k(-6)
a × b = -6k
While finding the angle between two vectors, substitute the magnitude of the vector value, Thus,
|a × b| = 6
Therefore, θ = sin-1[|a × b|/ |a| |b|]
θ = sin-1[ 6/ 5 .2 ]
θ = sin-1[ 3/ 5 ] = 36.87°
Hence, the angle between two vectors, a and b (θ) is 36.87°
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