Lecture 1: 13.1 13.2

Question 1

A two dimensional vector is notated as?

Answer 1

V = (P Q)->, where P = initial point and Q = terminal point.

Question 2

V is a vector with an arrow pointing from?

Answer 2

P to Q (initial point to terminal)

Question 3

Initial point and terminal point has coordinates?

Answer 3

(X, Y)

Question 4

What is a position vector?

Answer 4

A vector from the origin to a point, R.

Question 5

Parallel vectors?

Answer 5

Vectors of nonzero length if the lines through v and w are parallel. They do not need to point in the same direction.

Question 6

Translation in vectors?

Answer 6

When a vector is moved without changing the magnitude and direction (different base point).

Question 7

Equivalent vectors are those that?

Answer 7

Have the same direction and magnitude.

Question 8

Every vector v is or is not equivalent to a position vector?

Answer 8

Is

Question 9

Components of a Vector (a1, b1) and Q = (a2, b2), are the quantities

Answer 9

a = a2 − a1 (x-component), b = b2 − b1 (y-component)

Question 10

The pair of components is denoted by?

Answer 10

⟨a, b⟩.

Question 11

Zero vector?

Answer 11

A vector with no length and without direction.

Question 12

Vector sum v + w is defined when?

Answer 12

v and w have the same base point.

Question 13

What is x + w when the tail of w is on the head of x?

Answer 13

It is the vector from the tail of x and the head of w.

Question 14

Parallelogram law?

Answer 14

v + w if the tail of x and w are the same but pointing different directions, the v + w vector will have the same tail but will point exactly in the middle of v and w.

Question 15

How to add several vectors?

Answer 15

Translate each position vector in which the terminal is the initial of the next vector. v = v2 + v2 + … + v_n. The new vector, v will be a position vector pointing to the terminal of the last vector, v_n.

Question 16

Vector subtraction?

Answer 16

v − w is carried out by adding −w to v.

Question 17

∥λv∥ = ?

Answer 17

|λ| ∥v∥

Question 18

A vector w
is parallel to v if and only if?

Answer 18

w = λv for some nonzero scalar λ.

Question 19

Vector v points in the same/opposite direction if lambda > 0 and same/opposite direction if lambda < 0?

Answer 19

Same, different.

Question 20

Vector Operations Using Components: If v = ⟨a, b⟩ and w = ⟨c, d⟩, then for addition, subtraction, coefficients, and addition of 0? 4•

Answer 20

(i) v+w=⟨a+c,b+d⟩
(ii) v−w=⟨a−c,b−d⟩
(iii) λv = ⟨λa, λb⟩
(iv) v+0=0+v=v

Question 21

if P = (a1, b1) and Q = (a2, b2)?

Answer 21

PQ->=OQ->−OP-> =⟨a2,b2⟩−⟨a1,b1⟩=⟨a2 −a1,b2 −b1⟩

Question 22

THEOREM 1 Basic Properties of Vector Algebra For all vectors u, v, w and for all
scalars λ? Commutative law, associative law, distributive law? 3•

Answer 22

Commutative Law: v + w = w + v

Associative Law: u + (v + w) = (u + v) + w

Distributive Law for Scalars: λ(v + w) = λv + λw

Question 23

A linear combination of vectors v and w is a vector?

Answer 23

rv + sw

Question 24

Linear combination as system of linear equations?

Answer 24

{rv1 + sw1 = u1
{rv2 + sw2 = u2

Question 25

e_v is?

Answer 25

A unit vector in the direction v

Question 26

If i = ⟨1,0⟩, j = ⟨0,1⟩, then v, which is the linear combination vector, is?

Answer 26

v = ⟨a, b⟩ = ai + bj, in which a and b are scalers of i and j.

Question 27

Octant?

Answer 27

Is one of the eight divisions in a 3d coordinate space divided by four planes throughout each one of the axis.

Question 28

Vector addition is commutative, is associative, and satisfies the distributive property with respect to scalar multiplication?

Answer 28

Is commutative, is associative, and satisfies the distribution property.