Final answer:
To compute the cross product a × b for vectors a = (8, 0, -5) and b = (0, 7, 0), use the appropriate components in the cross product formula. The resulting vector is (35, 0, 56), indicating the direction and magnitude of the cross product.
Step-by-step explanation:
To find the cross product a × b for vectors a = (8, 0, -5) and b = (0, 7, 0), we need to apply the properties of the cross product such as distributive property and antocommutative property, along with the formula provided:
Č = Ḃ × B = (Ay B₂ – Az By)Î + (Az Bx − Ax Bz)Ḕ + (Ax By – AyBx)Ê.
Using the components of vectors a and b:
- Ay = 0, Az = -5, Ax = 8
- By = 7, Bx = 0, Bz = 0
And substituting these values into the formula, we get:
Č = (0 * 0 - (-5) * 7)Î + ((-5) * 0 - 8 * 0)Ḕ + (8 * 7 - 0 * 0)Ê
Č = (0 + 35)Î + (0 - 0)Ḕ + (56 - 0)Ê
Č = 35Î + 0Ḕ + 56Ê
So the cross product a × b is the vector (35, 0, 56).