Cross Product Calculator
Cross product of two vectors
This calculator can be used to calculate the cross product of two or more vectors. The vectors can be specified in i,j,k format or angle and magnitude format.
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A cross product is a vector multiplication which will always result in another vector.
Cross product formula
Cross product of two vectors can be calculated by matrix method or direct formula, both of which will be discussed.
1) Cross product Matrix method
If vector V1 = a1 i + b1 j + c1 k
and vector V2 = a2 i + b2 j + c2 k then cross product is given by the determinant of the below matrix.
\overline{V}_{1} \times \overline{V_{2}}=\left[\begin{array}{lll} i & j & k \\ a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \end{array}\right]alternatively this can be written as formula :
\overline{V_{1}} \times \overline{V_{2}}=\left(b_{1} c_{2}-b_{2} c_{1}\right) * \hat{\imath}-\left(a_{1} c_{2}-a_{2} c_{1}\right) * \hat{\jmath}+\left(a_{1} b_{2}-a_{2} b_{1}\right) * \hat{k}2) Cross product of unit vectors method
The cross product of unit vectors can be calculated from the given circle. As it is seen i x j = k; j x i = -k; j x k = i; k x j = -i; k x i = j; i x k = -j.
Using these rules we can find the cross product of two vectors.
Right hand thumb rule for vectors
According to the right hand thumb rule if the finger curl in the direction of Vector 1 to Vector 2, then the direction of thumb gives the direction of cross product of two vectors.
Cross product magnitude
If two vectors seperated by angle theta represented as a parallelogram, then the cross product magnitude is given by the area of the parallelogram.
The magnitude can also be given by the formula \text { Magnitude }=\left|V_{1}\right| *\left|V_{2}\right| * \sin \theta
