6.6 Operations with Algebraic Vectors in 2D
Chapter
Chapter 6
Section
6.6
Solutions 33 Videos

For A(-1, 3) and B(2, 5), draw a coordinate plane and place the points on the graph.

• Draw vectors \vec{AB} and \vec{BA}, and give vectors in component form equivalent to each of these vectors.
1.06mins
Q1a

For A(-1, 3) and B(2, 5), draw a coordinate plane and place the points on the graph.

Determine |\vec{OA}| and |\vec{OB}|.

0.43mins
Q1b

For A(-1, 3) and B(2, 5), draw a coordinate plane and place the points on the graph.

• Calculate |\vec{AB}| and state the value of |\vec{BA}|.
0.39mins
Q1c

Draw the vector \vec{OA} on a graph, where point A has coordinates (6, 10).

Draw the vectors m\vec{OA}, where m =\displaystyle{\frac{1}{2}}, -\displaystyle{\frac{1}{2}}, 2, and -2.

1.35mins
Q2a

Draw the vector \vec{OA} on a graph, where point A has coordinates (6, 10).

Which of these vectors have the same magnitude?

0.23mins
Q2b

For the vector \vec{OA}= 3\vec{i} -4\vec{j}, calculate |\vec{OA}|.

0.22mins
Q3

If a\vec{i} + 5\vec{j} = (-3, b), determine the values of a and b.

0.15mins
Q4a

Calculate |(-3, b)| after finding b.

0.17mins
Q4b

If \vec{a} = (-60, 11) and \vec{b}= (-40, -9), calculate each of the following:

a) |\vec{a}| and |\vec{b}|

0.24mins
Q5a

If \vec{a} = (-60, 11) and \vec{b}= (-40, -9), calculate each of the following:

|\vec{a} + \vec{b}| and |\vec{a} - \vec{b}|

1.07mins
Q5b

Find a single vector equivalent to each of the following:

2(-2, 3) + (2, 1)

0.14mins
Q6a

Find a single vector equivalent to each of the following:

-3(4, -9) - 9(2, 3)

0.24mins
Q6b

Find a single vector equivalent to each of the following:

-\displaystyle{\frac{1}{2}}(6, -2) \displaystyle{\frac{2}{3}}(6, 15)

0.27mins
Q6c

Given \vec{x} = 2\vec{i}-\vec{j} and \vec{y}=-\vec{i}+5\vec{j} , find a vector equivalent to each of the following:

3\vec{x} - \vec{y}

0.35mins
Q7a

Given \vec{x} = 2\vec{i}-\vec{j} and \vec{y}=-\vec{i}+5\vec{j} , find a vector equivalent to each of the following:

-(\vec{x} + 2\vec{y}) + 3(-\vec{x} -3\vec{y})

0.51mins
Q7b

Given \vec{x} = 2\vec{i}-\vec{j} and \vec{y}=-\vec{i}+5\vec{j} , find a vector equivalent to each of the following:

2(\vec{x} + 3\vec{y}) -3(\vec{y} + 5\vec{x})

0.47mins
Q7c

Given \vec{x} = 2\vec{i}-\vec{j} and \vec{y}=-\vec{i}+5\vec{j}, determine

|\vec{x} + \vec{y}|

0.18mins
Q8a

Given \vec{x} = 2\vec{i}-\vec{j} and \vec{y}=-\vec{i}+5\vec{j}, determine

|\vec{x} - \vec{y}|

0.33mins
Q8b

Given \vec{x} = 2\vec{i}-\vec{j} and \vec{y}=-\vec{i}+5\vec{j}, determine

|2\vec{x} - 3\vec{y}|

0.37mins
Q8c

Given \vec{x} = 2\vec{i}-\vec{j} and \vec{y}=-\vec{i}+5\vec{j}, determine

|3\vec{y} - 2\vec{x}|

0.39mins
Q8d

a) For each of the vectors shown below, determine the components of the related position vector.

b) Determine the magnitude of each vector.Determine the magnitude of each vector.

2.11mins
Q9

Parallelogram OBCA is determined by the vectors \vec{OA}=(6, 3) and \vec{OB}=(11, -6).

a) Determine \vec{OC}, \vec{BA}, and \vec{BA}.

b) Verify that |\vec{OA}|= |\vec{BA}|.

2.48mins
Q10

\triangle ABC has vertices at A(2, 3), B(6, 6) and C(-4, 11).

a) Sketch and label each of the points on a graph.

b) Calculate teach of the lengths |\vec{AB}|, |\vec{AC}|, and |\vec{CB}|.

1.36mins
Q11ab

\triangle ABC has vertices at A(2, 3), B(6, 6) and C(-4, 11).

Verify that triangle ABC is a right triangle.

0.41mins
Q11c

A parallelogram has three of its vertices at A(-1, 2) ,B(7, -2), and C(2, 8).

a) Draw a grid and locate each of these points.

b) On your grid, draw the three locations for a fourth point that would make a parallelogram with points A, B, and C.

c) Determine all possible coordinates for the point described in part b.

2.23mins
Q12

Determine the value of x and y in each of the following:

a) 3(x, 1) -5(2, 3y) = (11, 33)

b) -2(x, x + y) - 3(6, y) = (6, 4)

0.41mins
Q13a

Determine the value of x and y in each of the following:

-2(x, x + y) - 3(6, y) = (6, 4)

1.07mins
Q13b

Rectangle ABCD has vertices at A(2, 3), B( -6, 9), C(x, y), and D(8, 11).

a) Draw a sketch of the points A, B, and D, and locate point C on your graph.

b) Explain how you can determine the coordinates of point C.

2.56mins
Q14

A(5, 0) and B(0, 2) are points on the x- and y-axes, respectively.

Find the coordinates of point P(a, 0) on the x-axis such that |\vec{PA}| = |\vec{PB}|.

1.29mins
Q15a

A(5, 0) and B(0, 2) are points on the x- and y-axes, respectively.

• Find the coordinates of point on the y-axis such that |\vec{QB}| = |\vec{QA}|.
1.27mins
Q15b

Find the components of the unit vector in the direction opposite to \vec{PQ}, where \vec{OP} = (11, 19) and \vec{OQ} = (2, -21).

0.28mins
Q16

Parallelogram OPQR is such that \vec{OP} = (-7, 24) and \vec{OR} = (-8, -1).

Determine the angle between the vectors \vec{OR} and \vec{OP}.

Parallelogram OPQR is such that \vec{OP} = (-7, 24) and \vec{OR} = (-8, -1).
Determine the angle between the diagonals \vec{OQ} and \vec{RP}.