Given the following two vectors in R^{3}: calculate the cross product X × Y

X = 8i - 2j + 13k

Y = 3i + 5j - k

Write the coefficients as a matrix

i

j

k

x_{1}

x_{2}

x_{3}

y_{1}

y_{2}

y_{3}

→

i

j

k

8

-2

13

3

5

-1

Evaluate Cross Product Formula

X × Y = (x_{2}y_{3} - x_{3}y_{2})i + (x_{3}y_{1} - x_{1}y_{3})j + (x_{1}y_{2} - x_{2}y_{1})k

X × Y = (-2 x -1 - 13 x 5)i + (13 x 3 - 8 x -1)j + (8 x 5 - -2 x 3)k

X × Y = (2 - 65)i + (39 - -8)j + (40 - -6)k

X × Y = - 63i + 47j + 46k

Parallel Check:

Since X × Y <> 0: X and Y are not parallel

Final Answer

X × Y = - 63i + 47j + 46k Since X × Y <> 0: X and Y are not parallel

What is the Answer?

X × Y = - 63i + 47j + 46k Since X × Y <> 0: X and Y are not parallel

How does the Cross Product Calculator work?

Free Cross Product Calculator - Given two vectors A and B in R^{3}, this calculates the cross product A × B as well as determine if the two vectors are parallel This calculator has 6 inputs.

What 1 formula is used for the Cross Product Calculator?

X × Y = (x_{2}y_{3} - x_{3}y_{2})i + (x_{3}y_{1}x_{1}y_{3})j + (x_{1}2x_{2}y_{1})k