Cross Product Calculator
The cross product of the two arrows is defined as the third arrow that is perpendicular to the two original arrows.
What is Cross Product Calculator?
'Cuemath's Cross Product Calculator' is an online tool that helps to calculate the cross product of the given two vectors. Cuemath's online Cross Product Calculator helps you to calculate the cross product in a few seconds.
How to Use Cross Product Calculator?
Please follow the below steps to calculate the cross product:
- Step 1: Enter the coefficients of two vectors in the given input boxes.
- Step 2: Click on the "Calculate" button to calculate the cross product.
- Step 3: Click on the "Reset" button to clear the fields and enter the different values.
How to Find Cross Product Calculator?
Vectors are quantities with both magnitude and direction. Vectors help to simultaneously represent different quantities in the same expression.
The standard form of representation of a vector is:
a = a1i^ + a2j^ + a3k^
b = b1i^ + b2j^ + b3k^
Where a1, b1, c1, and a2, b2, c2 are numeric values and i^, j^, k^ are the unit vectors along the x-axis, y-axis, and z-axis respectively.
When two vectors are multiplied with each other and the product is also a vector quantity, then the resultant vector is called the cross product or the vector product. Cross product is represented by a × b. The cross product of two vectors is given by:
Cross product(a × b) = i(a2b3 − a3b2) − j(a1b3 − a3b1) + k(a1b2 − a2b1)
Find the cross product of two vectors a = 4i + 2j – 5k and b = 3i – 2j + k?
Given a = 4i + 2j – 5k and b = 3i – 2j + k
a × b = i(a2b3 − a3b2) − j(a1b3 − a3b1) + k(a1b2 − a2b1)
= i((2 × 1) - (-5) × (-2)) - j((4 × 1 - (5) × (3)) + k((4) × (-2) - (2 × 3))
= i(2 - 10) - j(4 + 15) + k(-8 - 6)
= -8i - 19j - 14k
Therefore, the cross product of two vectors is -8i - 19j - 14k
Similarly, you can use the calculator to find the cross product of two vectors for the following:
- a = 4i + 2j - 5k and b = -1i + 4j - 3k
- a = -2i - 5k and b = -7i + j + k