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Consider three planes P1 : x-y + z = 1, ...

Consider three planes `P_1 : x-y + z = 1`, `P_2 : x + y-z=-1` and `P_3 : x-3y + 3z = 2` Let `L_1, L_2` and `L_3` be the lines of intersection of the planes `P_2 and P_3`, `P_3 and P_1 ` and `P_1 and P_2` respectively. ` `Statement 1: At least two of the lines `L_1, L_2 and L_3` are non-parallel . Statement 2:The three planes do not have a common point

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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. The point on the line (x-2)/1=(y+3)/(-2)=(z+5)/(-2) at a distance of 6...

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  2. Let A( vec a)a n dB( vec b) be points on two skew lines vec r= vec a+...

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  3. Consider three planes P1 : x-y + z = 1, P2 : x + y-z=-1 and P3 : x-3y ...

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  4. Consider the planes 3x-6y-2z-15 =0 and 2x+y-2z - 5=0 Statement 1:The ...

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  5. The length of projection of the line segment joining the points (1,0,-...

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  6. If P1:vec r.vecn1-d1=0 P2:vec r.vec n2-d2=0 and P3:vec r.vecn3-d3=0 ar...

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  7. Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z...

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  8. The point P is the intersection of the straight line joining the point...

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  9. A line l passing through the origin is perpendicular to the lines l1: ...

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  10. Two lines L1: x=5, y/(3-alpha)=z/(-2) and L2: x=alpha, y/(-1)=z/(2-alp...

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  11. The projection of point P( vec p) on the plane vec r. vec n=q is ( v...

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  12. The angle between i and line of the intersection of the plane vec r ....

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  13. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

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  14. The plane vec rdot vec n=q will contain the line vec r= vec a+lambd...

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  15. Consider triangle A O B in the x-y plane, where A-=(1,0,0),B-=(0,2,0)a...

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  16. Let vec a= hat i+ hat j and vec b=2 hat i- hat k , then the point of ...

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  17. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

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  18. The equation of the plane which passes through the line of intersect...

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  19. The coordinates of the point P on the line vec r=( hat i+ hat j+ h...

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  20. The ratio in which the line segment joining the points whose positio...

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