# Worksheet: Angle between Two Straight Lines in Space

In this worksheet, we will practice finding the angle between two straight lines in three dimensions using the formula.

Q1:

A straight line passes through the two points and , and a straight line passes through the two points and . Find the measure of the angle between the two lines, giving your answer to two decimal places if necessary.

Q2:

Find, to the nearest second, the measure of the angle between the straight line and the positive direction of the -axis.

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Q3:

Determine, to the nearest second, the measure of the angle between the two lines that have direction ratios of and .

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Q4:

Find the measure of the angle between the straight line , and the straight line , .

Q5:

Find, to the nearest second, the measure of the angle between the two straight lines and .

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Q6:

Find the measure of the angle between the two straight lines , , and , and round it to the nearest second.

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Q7:

Find the measure of the angle between the two straight lines whose direction cosines are and . Give your answer to the nearest second.

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Q8:

Find the measure of the angle between the two straight lines and .

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Q9:

If , and , , then find the value of .

Q10:

Given that a straight line passes through the origin and the point , determine the exact value of .

Note that is the measure of the angle between the straight line and the positive direction of the -axis.

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Q11:

If a straight line makes direction angles of measures with the -axis and with the -axis, then find the direction angle it makes with the -axis.

Q12:

Find, to the nearest second, the measure of the angle between the straight line and the positive direction of the -axis.

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• B
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• D

Q13:

Find, to the nearest second, the measure of the angle between the straight line and the positive direction of the -axis.

• A
• B
• C
• D

Q14:

Find, to the nearest second, the measure of the angle between the two straight lines and .

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• D

Q15:

Find, to the nearest second, the measure of the angle between the two straight lines and .

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• D

Q16:

A straight line passes through the two points and , and a straight line passes through the two points and . Find the measure of the angle between the two lines, giving your answer to two decimal places if necessary.

Q17:

A straight line passes through the two points and , and a straight line passes through the two points and . Find the measure of the angle between the two lines, giving your answer to two decimal places if necessary.

Q18:

Which of the following gives the direction cosines of a straight line?

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• B
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• E

Q19:

Given that , , and are the direction cosines of a straight line, find the value of .

Q20:

If the direction angles of a straight line are , , and , then find the value of .