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Worksheet: 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 size of the angle between the two lines, giving your answer to two decimal places if necessary.
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Q2:
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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Q3:
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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Q4:
Determine, to the nearest second, the size of the angle between the two lines that have direction ratios of and .
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Q5:
Determine, to the nearest second, the size of the angle between the two lines that have direction ratios of and .
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Q6:
Determine, to the nearest second, the size of the angle between the two lines that have direction ratios of and .
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Q7:
Find the size of the angle between the straight line , and the straight line , .
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Q8:
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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Q9:
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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Q10:
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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Q11:
Find, to the nearest second, the size of the angle between the two straight lines and .
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Q12:
Find, to the nearest second, the size of the angle between the two straight lines and .
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Q13:
Find, to the nearest second, the size of the angle between the two straight lines and .
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Q14:
Find the size of the angle between the two straight lines , , and , and approximate it to the nearest second.
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Q15:
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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Q16:
Find the size of the angle between the two straight lines and .
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Q17:
If , and , , then find the value of .