Find a single vector equivalent to each expression below.
a) 5(0, -2, -4) - 4(3,8,0)
Please show me all steps so I can understand it.
Nevermind I got it.
(-12, -42, -20)
To find a single vector equivalent to the given expression, we need to simplify it by performing the scalar multiplication and vector subtraction.
a) 5(0, -2, -4) - 4(3, 8, 0)
Step 1: Perform scalar multiplication
5(0, -2, -4) = (0*5, -2*5, -4*5) = (0, -10, -20)
4(3, 8, 0) = (3*4, 8*4, 0*4) = (12, 32, 0)
Step 2: Perform vector subtraction
(0, -10, -20) - (12, 32, 0) = (0-12, -10-32, -20-0) = (-12, -42, -20)
Therefore, a single vector equivalent to the expression 5(0, -2, -4) - 4(3,8,0) is (-12, -42, -20).