Worksheet: Angle between Two Straight Lines in Three Dimensions

Q1:

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

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Q2:

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

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Q3:

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

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Q4:

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

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Q5:

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

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Q6:

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

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Q7:

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

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Q8:

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

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Q9:

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

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Q10:

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

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Q11:

Find the size of the angle between the two straight lines , , and , and approximate it to the nearest second.

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Q12:

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

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Q13:

If , and , , then find the value of .

Q14:

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

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Q15:

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

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Q16:

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

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Q17:

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

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