Chapter 11 - Vectors

Question 1

If PQ = RS, then what can you say about line segments PQ and RS?

Answer 1

They are equal in length and parallel

Question 2

What is the triangle law for vector addition?

Answer 2

AB + BC = AC

Question 3

PQ + QP = ?

Answer 3

0 zero vector

Question 4

If a vector is parallel to a, how can it be written?

Answer 4

ka, where k is a non-zero scalar

Question 5

To multiply a column vector by a scalar, what do you do?

Answer 5

Multiply each component by the scalar:

Question 6

Adding/subtracting two vectors eg

p + r

q s

Answer 6

p+r

q+s

Question 7

What are the unit vectors? And what is their length?

Answer 7

i = unit vector along x axis

j = unit vectors along y axis

length = 1

Question 8

Write the two-dimensional vector using unit vectors eg

p

q

Answer 8

pi + qj

Question 9

For the vector a = xi + yj, how do you calculate the magnitude?

Answer 9

Magnitude |a| = sq root (x² + y²)

Question 10

How do you calculate the unit vector of a?

Answer 10

a / |a|

Question 11

What is the position vector of a pont P with coordinates (p,q)?

Answer 11

OP = pi + qj

Question 12

How do you calculate AB from position vectors?

Answer 12

AB = AO + OB = - OA + OB = OB - OA

Question 13

If the point P divides the line segment AB in the ratio k:m, what is OP equal to?

Answer 13

OP = OA + k/(k+m) AB

= OA + k/(k+m) (OB - OA)

Question 14

If a and b are two non-parallel vectors and

pa + qb = ra + sb

what can you say?

Answer 14

p = r

q = s