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Class 12 Maths Practice Test - Angle between Two Lines
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Class 12 Maths Practice Test - Angle between Two Lines
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10 Questions

1. Find the value of p such that the lines
\(\frac{x-1}{3}=\frac{y+4}{p}=\frac{z-9}{1}\)
\(\frac{x+2}{1}=\frac{y-3}{1}=\frac{z-7}{-2}\)
are at right angles to each other.
2. If the equations of two lines L1 and L2 are \(\vec{r}=\vec{a_1}+λ\vec{b_1}\) and \(\vec{r}=\vec{a_2}+μ\vec{b_2}\), then which of the following is the correct formula for the angle between the two lines?
3. Find the angle between the lines \(\vec{r}=2\hat{i}+6\hat{j}-\hat{k}+λ(\hat{i}-2\hat{j}+3\hat{k})\) and \(\vec{r}=4\hat{i}-7\hat{j}+3\hat{k}+μ(5\hat{i}-3\hat{j}+3\hat{k})\).
4. Find the value of p such that the lines \(\frac{x+11}{4}=\frac{y+3}{-2}=\frac{z-3}{4} \,and \,\frac{x-3}{p}=\frac{y+12}{2}=\frac{z-3}{-12}\) are at right angles to each other.
5. If L1 and L2 have the direction ratios \(a_1,b_1,c_1 \,and \,a_2,b_2,c_2\) respectively then what is the angle between the lines?
6. Find the angle between the two lines if the equations of the lines are
\(\vec{r}=\hat{i}+\hat{j}+\hat{k}+λ(3\hat{i}-\hat{j}+\hat{k}) \,and \,\vec{r}=4\hat{i}+\hat{j}-2\hat{k}+μ(2\hat{i}+3\hat{j}+\hat{k})\)
7. Find the angle between the lines.
\(\frac{x+2}{1}=\frac{y+5}{6}=\frac{z-3}{2}\)
\(\frac{x-4}{5}=\frac{y-3}{-2}=\frac{z+3}{1}\)
8. If two lines L1 and L2 with direction ratios \(a_1,b_1,c_1 \,and \,a_2,b_2,c_2\) respectively are perpendicular to each other then
\(a_1 a_2+b_1 b_2+c_1 c_2=0\)
9. Find the angle between the pair of lines \(\frac{x-3}{5}=\frac{y+7}{3}=\frac{z-2}{2} \,and \,\frac{x+1}{3}=\frac{y-5}{4}=\frac{z+2}{8}\).
10. If two lines L1 and L2 are having direction cosines \(l_1,m_1,n_1 \,and \,l_2,m_2,n_2\) respectively, then what is the angle between the two lines?

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