6.6 Operations with Algebraic Vectors in 2D
Chapter
Chapter 6
Section
6.6
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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.
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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}|.

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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}|.
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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.

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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?

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0.23mins
Q2b

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

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0.22mins
Q3

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

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0.15mins
Q4a

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

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0.17mins
Q4b

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

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

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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}|

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1.07mins
Q5b

Find a single vector equivalent to each of the following:

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

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0.14mins
Q6a

Find a single vector equivalent to each of the following:

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

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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)

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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}

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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})

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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})

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0.47mins
Q7c

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

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

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0.18mins
Q8a

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

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

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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}|

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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}|

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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.

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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}|.

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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}|.

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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.

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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.

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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)

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0.41mins
Q13a

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

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

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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.

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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}|.

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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}|.
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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).

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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}.

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2.53mins
Q17a

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}.

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2.45mins
Q17b