Guided Example #1 - Vectors

Two anchors are holding a ship in place and their forces acting on the ship are represented by vectors A and B as follows:

$A = 2 i + 5 j - 4 k$ $A = 2 i + 5 j - 4 k$ and $B = - 2 i - 3 j - 5 k$ $B = - 2 i - 3 j - 5 k$

If we were to replace the 2 anchors with 1 single anchor, what vector represents that single vector?

a. $4 i + 8 j + k$ $4 i + 8 j + k$
b. $8 j - 9 k$ $8 j - 9 k$
c. $4 i + 8 j - 9 k$ $4 i + 8 j - 9 k$
d. None of the above

The correct answer is D. To see why, view each of the steps below.

Step 1

The problem just requires us to add the vectors to get the single resultant vector.
$R = (2 + - 2) i + (5 - 3) j + (- 4 - 5) k$ $R = (2 + - 2) i + (5 - 3) j + (- 4 - 5) k$
$A + B = 0 i + 2 j - 9 k$ $A + B = 0 i + 2 j - 9 k$
$= 2 j - 9 k$ $= 2 j - 9 k$

All Steps

The problem just requires us to add the vectors to get the single resultant vector.

R = (2 + - 2) i + (5 - 3) j + (- 4 - 5) k

$R = (2 + - 2) i + (5 - 3) j + (- 4 - 5) k$

A + B = 0 i + 2 j - 9 k

$A + B = 0 i + 2 j - 9 k$

= 2 j - 9 k

$= 2 j - 9 k$