Direction Cosines of a Line Passing through Two Points

Q. 20. find distance of the point (8, -6) from the line 8x-6y-10=0

Q. 48. Find the length and the foot of the perpendicular drawn from the point (2, -1, 5)to the line (x-1)/10=(y+2)/-4=(z+8)/-1.

Q. 10. P and Q trisect the line segment joining the points (2, 1) and (5, -8) If the point P lies on 2x-y+k=0, find k.

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. A point “P” is located in three dimensional coordinate plane such that the angles made by OP with positive direction of X - axis is ${30}^{\circ }$ and Y- axis is ${60}^{\circ }$ then find the angle made by OP with positive direction of Z - axis, where “O” is origin.

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. 11. The distance of the point (2, 3) from the line x-2y + 5=0 measured in a direction parallel to the line x-3y=0 is

Q. A line passing through the points (a, 2a) and (−2, 3) is perpendicular to the line 4x + 3y + 5 = 0; find the value of a.

Q. Conordinates of a point which is at 3 units distane from the point (1, –3) on the line 2x + 3y + 7 = 0 is/are.

(A) $\left(1+\frac{9}{\sqrt{13}},3-\frac{6}{\sqrt{13}}\right)$ (B) $\left(1-\frac{9}{\sqrt{13}},-3+\frac{6}{\sqrt{13}}\right)$

(C) $\left(1+\frac{9}{\sqrt{13}},-3-\frac{6}{\sqrt{13}}\right)$ (D) $\left(1-\frac{9}{\sqrt{13}},3-\frac{6}{\sqrt{13}}\right)$

Q. Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.

Q. Write the length of the chord of the parabola y² = 4ax which passes through the vertex and is inclined to the axis at $\frac{\mathrm{\pi }}{4}$.