Inclination of a Line

Q.

Find the equation of the line which pass through $(4,5)$ and makes equal angles with the lines $5y=12x+6$ and $3x=4y+7$.

Q. A straight line is equally inclined to all the three coordinate axes. Then the acute angle made by the line with the $y$-axis is:

1. ${\cos }^{-1}\left(\frac{1}{3}\right)$
2. ${\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
3. ${\cos }^{-1}\left(\frac{2}{\sqrt{3}}\right)$
4. $\frac{\pi }{4}$

Q. The equation of straight line passing through point $A(-1,3,-2)$ and equally inclined to positive co-ordinate axes is

1. $x+1=y-3=z+2$
2. $\sqrt{3}x+1=\sqrt{3}y-3=\sqrt{3}z+2$
3. $x+\sqrt{3}=y-3\sqrt{3}=z+2\sqrt{3}$
4. $\frac{x+1}{\sqrt{3}}=\frac{y-3}{-\sqrt{3}}=\frac{z+2}{-\sqrt{3}}$

Q.

The inclination of the straight line passing through the point $(-3,6)$ and the mid-point of the line joining the point $(4,-5)$ and $(-2,9)$ is

1. $\frac{\pi }{4}$

2. $\frac{\pi }{6}$

3. $\frac{\pi }{3}$

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

Q. If $AB=BA$ for any two square matrices, prove by mathematical induction that $(AB{)}^n=A^n{B}^n$

Q. Find the angle between the following pair of lines
$\frac{x}{2}=\frac{y}{2}=\frac{z}{1}and\frac{z-5}{4}=\frac{y-2}{1}=\frac{z-3}{8}$

Q.

Find the angle between X-axis and the line joining the points (3, -1) and (4, -2).

Q. Find the slope of the line whose inclination is ${60}^o$.

Q. The gradient of the line joining the points on the curve $y=x^2+2x$ whose abscissa are 1 and 3, is

1. 6
2. 5
3. 4
4. 3

Q.

If the acute angle between two line is $\frac{\pi }{4}$ and slope of one of them

is $\frac{1}{2}$. Find the slope of the other line.

1. 2

2. 

3. 3

4. 

Q.

Which quadrant does the given angle $-127$ degrees lie?

Q. Find the distance of the line $4x-y=0$ find the point $P(4,1)$ measured along the line making an angle of ${135}^o$ with the positive x-axis.

Q.

The angle between the lines represented by the equation $4x^2-24xy+11y^2=0$are

1. 

2. 

3. 

4. 

Q. Find the angles between the lines
$x+\sqrt{3}y=1$

Q. Find inclination (in degrees) of a line perpendicular to y-axis.

Q. If $A(9,-9),C(1,-3)$ are the end points of hypotenuse of a right angled isosceles triangle, then the third vertex is

1. $(8,-2)$
2. $(8,-8)$
3. $(-8,2)$
4. $(0,0)$

Q.

Q. Find the inclination of a line whose slope is
$\frac{1}{\sqrt{3}}$

Q. Find inclination (in degrees) of a line parallel to x-axis.

Q. The equation of the lines through $(-1,-1)$ and making an angle ${45}^o$ with the line $x+y=0$ are

1. $x+1=0,x-y=0$
2. $x+1=0,y+1=0$
3. $x-y=0,y+1=0$
4. $x+y+2=0,y+1=0$

Q. If the segment intercepted by the parabola $y=4ax$ with the line $lx+my+n=0$ subtends a right angle at the vertex then

1. $4al+n=0$
2. $4am+n=0$
3. $al+n=0$
4. $4al+4am+n=0$

Q. Find the angle which the straight line $y=\sqrt{3}x-4$ makes with y-axis.

Q. Find the inclination of a line whose slope is: $\sqrt{3}$.

Q. If a line makes angles ${90}^o$, ${60}^o$ and ${30}^o$ with the positive direction of x, y and z axis respectively find its direction cosines.

Q. If $\theta$ is an acute angle between the lines $y=2x+3,y=x+1$, then the value of $\tan \theta =$

1. $2/3$
2. $1/3$
3. $3/4$
4. $1/2$

Q. Find the angles between the lines
$x-\sqrt{3}y=-1$

Q. Find the slope of a non-vertical line $ax+by+c=0$

Q. The gradient of the line joining the points on the curve $y=x^2+2x$ whose abscissa are 1 and 3, is

1. 6
2. 5
3. 4
4. 3

Q. Find the angles between the lines
$x+\sqrt{3}y=5$

Q. Let $P=(-1,0),Q=(0,0),andR=(3,3\sqrt{3})$ be three points. Then the equation of the bisector of $\angle PQR$ is

1. $x+\left(\frac{\sqrt{3}}{2}\right)y=0$
2. $\left(\frac{\sqrt{3}}{2}\right)x+y=0$
3. $\sqrt{3}x+y=0$
4. $x=\sqrt{3}y=0$