What is the vector product of A=2i + 3j + 1k and B=1i - 3j - 2k?
The vector product, also known as the cross product, of two vectors A and B is a vector that is perpendicular to both A and B. To find the vector product, you can use the following formula:
A × B = (Ay * Bz - Az * By)i + (Az * Bx - Ax * Bz)j + (Ax * By - Ay * Bx)k
where Ax, Ay, Az are the components of vector A, and Bx, By, Bz are the components of vector B.
Let's calculate the vector product of vectors A and B:
A = 2i + 3j + 1k
B = 1i - 3j - 2k
Plugging the values into the formula, we get:
A × B = ((3 * -2) - (1 * -3))i + ((1 * 1) - (2 * -2))j + ((2 * -3) - (3 * 1))k
= (-6 + 3)i + (1 + 4)j + (-6 - 3)k
= -3i + 5j - 9k
So, the vector product of vectors A and B is -3i + 5j - 9k.