Vectors — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Add or subtract corresponding components.

a + b = (2, 6); a − b = (4, 2)

Question 2

(a)Multiply each component by 2.

2a = (6, 8)

Question 3

(a)Magnitude = √(x² + y²).

√(3²+4²) = √25 = 5

Question 4

(a)Multiply each vector by its scalar, then subtract component-wise.

3(2,−3) − 2(5,1) = (6,−9) − (10,2) = (−4, −11)

Question 5

(a)Magnitude = √(x²+y²).

√(5²+1²) = √26 ≈ 5.10

Question 6

(a)Find |a| = √(4+9)=√13, then divide each component by this magnitude.

(2/√13, −3/√13)

Question 7

(a)In a parallelogram OABC, AB is parallel and equal to OC.

AB = c

Question 8

(a)Magnitude = √(x²+y²).

√(16+1) = √17 ≈ 4.12

Question 9

(a)Double b's components, then add to a.

(4,−1) + (−4,6) = (0, 5)

Question 10

(a)AC = AO + OC = −a + c.

AC = c − a

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