Conditions for a system of linear equations to have a unique solution

Q.

The lines $ax+by+c=0$, where $3a+2b+4c=0$are concurrent at the point

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

2. $(1,3)$

3. $(3,1)$

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

Q.

Find the shortest distance between the lines

Q.

If the equations in a system of two linear equations in two variables are graphed, each graph will be a line. Which of the following System of Linear equations will have only one solution ?

1. Parallel lines
2. Coincidental lines
3. Intersecting lines
4. All of the above

Q.

Find the shortest distance between the lines and

Q. This belongs to Dc's and dr's
if the dc's of two lines are connected by relations l +m-n =0
6ln -12lm+ mn =0 then dc's of two line are.....?
(1/root14, 2/root14, 3/root14) , (1/root26, 3/root26, 4/root26)

Q. -6x + 4y = 2 ;
3x + 2y = -1
Consider the system of equations above. If (x, y) is a solution of the equations above, then how many possible values are there for (x, y) ?

1. No solution
2. Infinitely many solutions
3. One solution
4. None of the above

Q.

Find the shortest distance between the lines whose vector equations are

Q. What does the equations 4x+3y-2z+5 = 0 and 3y-4x+2z+10 = 0 together represent?

1. Straight line
2. Point
3. One side of two intersecting planes
4. Intersection of two planes

Q.

Find the shortest distance between lines

and.

Q. $4(81+x)=\left(3k\right)x$
In the above equation, $k$ is a constant. For what value of $k$, is there a unique solution to the equation?

1. Any real value
2. Any real value except 4/3
3. Any real value between -4/3 and 4/3
4. k = 4/3

Q.

Examine the consistency of the system of equations.

2x − y = 5

x + y = 4

Q. Write the order of the differential equation of all non-horizontal lines in a plane.

Q.

Given the equation: $\frac{(a-c)}{(x-a)}=m$, solve for $x$.

Q.

Find the shortest distance between the lines whose vector equations are

Q.

Find the shortest distance between the lines whose vector equations are

Q. solve

$$\begin{gathered} Considerthelines \\ \overline{r}=(i+2j-2k)+\lambda (i+2j)and \\ \overline{r}=(i+2j-2k)+\mu (2j-k) \end{gathered}$$
a) Find the angle between the lines.
b) Find a vector perpendicular to both the lines.
c) Find the equation of the line passing through the point of intersection of lines and perpendicular to both the lines.

Q.

Find the values of p so the line and

are at right angles.

Q. If there is a system of 3 equations of two variables so is it true that they will be consistent if and only if the three lines represented by the three equations are concurrent , else in every other case the system will be inconsistent, be it 2 parallel , all three parallel , or no line parallel but all three not instersecting at single point?

Q. Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.

Q. Find the differential equation of all non-vertical lines in a plane.

Q. the lines 2(x-y) = 3, 6x +5 = 6y are parellel, state true or false