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In this lesson, we will learn how to find the angle between two straight lines in three dimensions.

Q1:

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

Q2:

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

Q3:

Q4:

Q5:

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

Q6:

Q7:

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.

Q9:

Q10:

Q11:

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

Q12:

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

Q13:

If 𝐿 ∶ 𝑥 = 0 1 , 𝑦 = 𝑧 and 𝐿 ∶ 𝑦 = 0 2 , 𝑥 = 𝑧 , then find the value of 𝜃 .

Q14:

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

Q15:

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

Q16:

Q17:

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