Find the angle between the following pair of lines:

Question 14 of 25intermediate🔧 ApplyShort Answer4 marks

(i)

$\frac{x-2}{2} = \frac{y-1}{5} = \frac{z+3}{-3}$ and $\frac{x+2}{-1} = \frac{y-4}{8} = \frac{z-5}{4}$

Answer

θ = cos⁻¹(26/9 $\sqrt{38}$ )

(ii)

$\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$ and $\frac{x-5}{4} = \frac{y-2}{1} = \frac{z-3}{8}$

Answer

θ = cos⁻¹(2/3)

Explanation

This question tests the application of the angle formula between two lines in Cartesian form. Students must identify direction ratios from the symmetric equations and apply the formula correctly. The absolute value ensures the acute angle is obtained.

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