Question

1a. Given that P = (5,4), Q = (7,3), R = (8,6), and S = (4,1), find the component form of the vector PQ + 3RS.

a. (-10,-16)
b. (-6,4)
c. (-2,-6)
d. (14,14)

1b. Use the information from 1a to find the magnitude of the vector PQ + 3RS.

a. 356
b. √26
c. 2√10
d. 2√89

2a. Given that P = (5,4), Q = (7,3), R = (8,6), and S = (4,1), find the component form of the vector PQ + 4RS.

a. (18,19)
b. (-2,-6)
c. (-14,-21)
d. (-18,-19)

2b. Use the information from 2a to find the magnitude of the vector PQ + 4RS.

a. 2√10
b. 7√10
c. √35
d. 637

3a. Given that P = (5,4), Q = (7,3), R = (8,6), and S = (4,1), find the component form of the vector PQ + 5RS.

a. (22,24)
b. (-2,-6)
c. (-18,-26)
d. (-22,-24)

3b. Use the information from 3a to find the magnitude of the vector PQ + 5RS.

a. 1000
b. 10√10
c. 2√11
d. 2√10

Answer 1

1a. A
1b. D
2a. C
2b. B
3a. C
3b. B

Answer 2

1a) a)
`\overrightarrow {\alpha} = (-10,-16)`, 1b)
`\| \overrightarrow {\alpha} \| = 2√(89)`, 2a)
`\overrightarrow {\alpha} = (-14,-21)`, 2b)
`\| \overrightarrow {\alpha} \| = 7√(13)`, 3a)
`\overrightarrow {\alpha} = (-18,-26)`, 3b)
`\| \overrightarrow {\alpha} \| = 10√(10)`

Explanation:

1a) The vectors
`\overrightarrow {PQ}` and
`\overrightarrow {RS}` are determined:

`\overrightarrow {PQ} = (7-5,3-4)`

`\overrightarrow {PQ} = (2, -1)`

`\overrightarrow {RS} = (4-8,1-6)`

`\overrightarrow {RS} = (-4, -5)`

The component form of the resultant vector is:

`\overrightarrow {\alpha} = (2 -12, -1-15)`

`\overrightarrow {\alpha} = (-10,-16)`

1b) The magnitude of the resultant vector is:

`\| \overrightarrow {\alpha} \| = \sqrt{(-10)^(2)+(-16)^(2)}`

`\| \overrightarrow {\alpha} \| = 2√(89)`

2a) The vectors
`\overrightarrow {PQ}` and
`\overrightarrow {RS}` are determined:

`\overrightarrow {PQ} = (7-5,3-4)`

`\overrightarrow {PQ} = (2, -1)`

`\overrightarrow {RS} = (4-8,1-6)`

`\overrightarrow {RS} = (-4, -5)`

The component form of the resultant vector is:

`\overrightarrow {\alpha} = (2 -16, -1-20)`

`\overrightarrow {\alpha} = (-14,-21)`

2b) The magnitude of the resultant vector is:

`\| \overrightarrow {\alpha} \| = \sqrt{(-14)^(2)+(-21)^(2)}`

`\| \overrightarrow {\alpha} \| = 7√(13)`

3a) The vectors
`\overrightarrow {PQ}` and
`\overrightarrow {RS}` are determined:

`\overrightarrow {PQ} = (7-5,3-4)`

`\overrightarrow {PQ} = (2, -1)`

`\overrightarrow {RS} = (4-8,1-6)`

`\overrightarrow {RS} = (-4, -5)`

The component form of the resultant vector is:

`\overrightarrow {\alpha} = (2 -20, -1-25)`

`\overrightarrow {\alpha} = (-18,-26)`

3b) The magnitude of the resultant vector is:

`\| \overrightarrow {\alpha} \| = \sqrt{(-18)^(2)+(-26)^(2)}`

`\| \overrightarrow {\alpha} \| = 10√(10)`