Direction Cosines of a Line Passing through Two Points

Q.

The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z is

1. $3\sqrt{10}$

2. $10\sqrt{3}$

3. $\frac{10}{\sqrt{3}}$

4. $\frac{20}{3}$

Q. Find the direction cosines of the line passing through the points
P (2, 3, 5) and Q (–1, 2, 4).

1. (-2, -1, -1)
2. $\left(\frac{3}{\sqrt{11}},\frac{1}{\sqrt{11}},\frac{1}{\sqrt{11}}\right)$
3. $\left(\frac{-3}{\sqrt{11}},\frac{-1}{\sqrt{11}},\frac{-1}{\sqrt{11}}\right)$
4. $\left(\frac{-3}{\sqrt{11}},\frac{1}{\sqrt{11}},\frac{1}{\sqrt{11}}\right)$

Q. The direction cosines of the line drawn from P(–5, 3, 1) to Q(1, 5, –2) is

1. $(6,2,-3)$
2. $(2,-4,1)$
3. $(-4,8,-1)$
4. $(\frac{6}{7},\frac{2}{7},-\frac{3}{7})$

Q. Find the direction cosines of the line passing through the points
P (2, 3, 5) and Q (–1, 2, 4).

1. (-2, -1, -1)
2. $\left(\frac{3}{\sqrt{11}},\frac{1}{\sqrt{11}},\frac{1}{\sqrt{11}}\right)$
3. $\left(\frac{-3}{\sqrt{11}},\frac{-1}{\sqrt{11}},\frac{-1}{\sqrt{11}}\right)$
4. $\left(\frac{-3}{\sqrt{11}},\frac{1}{\sqrt{11}},\frac{1}{\sqrt{11}}\right)$

Q.

A line with directiion ratios 2, 7, -5 is intercepted between the lines
$\frac{x-5}{3}=\frac{y-7}{-1}=\frac{z+2}{1}and\frac{x+3}{-3}=\frac{y-3}{2}=\frac{z-6}{4}$. Find the length intercepted between the given lines.___

1. $\sqrt{78}$

2. 9
3. $\sqrt{85}$
4. 10

Q. If a line passes through two points (1, 2, 3) & (4, 5, 6) then the direction cosines of that line would be -

1. $\frac{2}{\sqrt{3}},\frac{2}{\sqrt{3}},\frac{2}{\sqrt{3}}$
2. $\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}},\frac{1}{\sqrt{3}}$
3. $\frac{2}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}}$
4. $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$