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

**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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**Q13: **

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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**Q14: **

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

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**Q15: **

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

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**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.