Vector Equation for Straight Line

Q. let a=i+j, b=j+k and c=αa+βb.If the vectors i-2j+k, 3i+2j-k and c are coplanar then α/β equals

Q.

The shortest distance between the lines $\frac{x-1}{0}=\frac{y+1}{-1}=\frac{z}{1}$ and $x+y+z+1=0$, $2x-y+z+3=0$ is:

1. $1$

2. $\frac{1}{\sqrt{2}}$

3. $\frac{1}{\sqrt{3}}$

4. $\frac{1}{2}$

Q. The angle betweente lines 3x+y-7=0 and x+2y+9=0 is

Q. 3. The lines x=ay+b, z=cy+d and x=a1y+b1, z=c1y+d1 will be perpendicular if

Q. 39. Point z moves on curve |z-3i-4|+|z-5-12i|=82 value of |z|min+|z|max is 1) 10 2)18

Q. If vector a×b = 2i + 2j - k and vector 3a+b = 2i - 4j - 4k. Then find the minimum and maximum value of a.b ( ie the dot product of vector a and b).

Q. the length of the intercept made by the parabola 2y^2+6y=8-5x on y axis is a)7 b)5 c)3 d)1

Q. 30. Three lines px+qy+r=0, qx+ry+p=0, rx+py+q=0 are concurrent if

Q.

The equation of a line passing through the points 3i + 4j and i + 2j can be given by $\overrightarrow{r}=(1+2\lambda )i+(2+2\lambda )j.Here\lambda ϵIR$

1. True

2. False

Q. $\mathrm{If}\mathrm{two}\mathrm{lines}{L}_1=a_1+{\mathrm{\lambda b}}_1\mathrm{and}{L}_2=a_2+{\mathrm{\lambda b}}_2\mathrm{are}\mathrm{such}\mathrm{that}{b}_1\mathrm{is}\mathrm{parallel}\mathrm{to}{b}_2\mathrm{and}{a}_1\ne a_2,\mathrm{then}{L}_1\mathrm{and}{L}_2\mathrm{will}\mathrm{be}$

1. coincident lines
2. intersecting lines
3. parallel lines
4. perpendicular lines

Q. $\mathrm{In}\mathrm{the}\mathrm{given}\mathrm{two}\mathrm{lines}{L}_1=a_1+{\mathrm{\lambda b}}_1\mathrm{and}{L}_2=a_2+{\mathrm{\lambda b}}_2,\mathrm{if}{b}_1=b_2\mathrm{then}\mathrm{the}\mathrm{lines}\mathrm{will}\mathrm{be}\mathrm{definitely}\mathrm{parallel}.$

1. False
2. True