Chapter 12 Vectors

Question 1

What is a unit vector in the same direction as r = ai + bj?

Answer 1

Example: If r = 3i + 4j, the unit vector is (3/5)i + (4/5)j.

Question 2

How is the length (or modulus or magnitude) of the vector r written?

Answer 2

The length of the vector r is written as |r|

Example: If r = 3i + 4j, then |r| = 5.

Question 3

How is the vector AB defined?

Answer 3

The vector AB = b - a, where a and b are the position vectors of A and B.

Question 4

What is the position vector OP of a point P?

Answer 4

The position vector OP of a point P is the vector joining the origin to P.

Question 5

How is a resultant vector usually denoted?

Answer 5

A resultant vector is usually denoted by a double-headed arrow.

Question 6

How is the resultant of two or more vectors found?

Answer 6

The resultant of two or more vectors is found by the sum of the vectors.

Question 7

In what forms may a vector be specified?

Answer 7

A vector may be specified in component form (xi + yj or column vector ) or in magnitude-direction form (r, θ).

Question 8

How are unit vectors in the x and y directions denoted?

Answer 8

Unit vectors in the x and y directions are denoted by i and j, respectively.

Question 9

What is a unit vector?

Answer 9

A unit vector is a vector with magnitude 1.

Question 10

How are vectors typeset?

Answer 10

Vectors are typeset in bold, a or OA, or in the form (OA) with arrow above.

Question 11

What is a scalar quantity?

Answer 11

A scalar quantity has magnitude only.

Question 12

What is a vector quantity?

Answer 12

A vector quantity has magnitude and direction.

Question 13

What is the formula to calculate the magnitude of a vector?

Answer 13

Question 14

What is the formula to calculate a Unit Vector?

Answer 14