Question

Given that e= 2i – 5j + 9k and f= 8i + 15j + k, find 3f – 2e.

20i + 55j – 21k
28i + 55j – 15k
20i + 55j – 15k
20i + 35j – 15k

Answer 1

3f – 2e

Plug in 2i – 5j + 9k for e and 8i + 15j + k for f

3(8i + 15j + k) - 2(2i – 5j + 9k)

Distribute 3 and 2 inside their respective parentheses

(24i + 45j + 3k) - (4i - 10j + 18k)

Now distribute -1 (negative sign) inside the parentheses on the right

(24i + 45j + 3k) - 4i + 10j - 18k

Combine like terms

20i + 55j - 15k is your answer (third choice down)

Answer 2

Plug in "8i + 15j + k" for "f", and "2i – 5j + 9k" for "e"

3(8i + 15j + k) - 2(2i – 5j + 9k)

Distribute 3 to (8i + 15j + k) & - 2 to (2i – 5j + 9k)

3(8i + 15j + k) = 24i + 45j + 3k

-2(2i - 5j + 9k) = -4i + 10j - 18k

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Simplify. Combine like terms

24i - 4i + 45j + 10j + 3k - 18k

(24i - 4i) + (45j + 10j) + (3k - 18k)

20i + 55j - 15k is your answer, or (C)

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hope this helps