Given that e=8i-6j and f=4i+11j find 5f-2e Show your work.
Very straightforward ...
if e=8i-6j and f=4i+11j
then 5f - 2e
= 5(4i + 11j) - 2(8i - 6j)
= 20i + 55j - 16i + 12j
= 4i + 67j
To find the expression 5f - 2e, we need to multiply each term of f and e by their respective coefficients.
Given:
e = 8i - 6j
f = 4i + 11j
Step 1: Multiply each term of f by 5
5f = 5(4i + 11j)
= 20i + 55j
Step 2: Multiply each term of e by -2
-2e = -2(8i - 6j)
= -16i + 12j
Step 3: Subtract the result of -2e from 5f
5f - 2e = (20i + 55j) - (-16i + 12j)
= 20i + 55j + 16i - 12j
= (20i + 16i) + (55j - 12j)
= 36i + 43j
Therefore, 5f - 2e is equal to 36i + 43j.
To find the value of 5f - 2e, we need to perform scalar multiplication and vector subtraction.
First, let's find 5f by multiplying each component of f by 5:
5f = 5(4i + 11j)
= 20i + 55j
Next, let's find 2e by multiplying each component of e by 2:
2e = 2(8i - 6j)
= 16i - 12j
Now, we can subtract 2e from 5f:
5f - 2e = (20i + 55j) - (16i - 12j)
= 20i + 55j - 16i + 12j
= (20i - 16i) + (55j + 12j)
= 4i + 67j
Therefore, 5f - 2e = 4i + 67j.