Find an ordered triple to represent vector x in x = -6z+1/4y if vector y=<2,18,-4/5> and vector z = <-1/2, 3/4, -1/6> Please and thank you.
Multiple Choice:
a) <25/8, 0, 4/5>
b) <7/2, 0, 4/5>
c) <7/2, 0, 6/5>
d) <7/2, 33/8, 4/5>
To find the ordered triple that represents vector x in the equation x = -6z + 1/4y, we can substitute the given vectors y and z into the equation.
First, let's calculate -6z:
-6z = -6 * <-1/2, 3/4, -1/6>
= <6/2, -18/4, 6/6> (multiplying each component by -6)
= <3, -9/2, 1>
Next, let's calculate 1/4y:
1/4y = 1/4 * <2, 18, -4/5>
= <2/4, 18/4, -4/5> (multiplying each component by 1/4)
= <1/2, 9/2, -4/5>
Finally, let's add -6z and 1/4y to get vector x:
x = -6z + 1/4y
= <3, -9/2, 1> + <1/2, 9/2, -4/5>
= <3 + 1/2, -9/2 + 9/2, 1 - 4/5>
= <7/2, 0, 1/5>
The ordered triple representing vector x is <7/2, 0, 1/5>.
Out of the given choices, none of them match the calculated value of <7/2, 0, 1/5>.