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Prove that the four points having positi...

Prove that the four points having position vectors are non-coplanar: ` hat i+2 hat j+3 hat k ,2\ hat i+ hat j+3 hat k\ a n d\ hat i+ hat j+ hat k`

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Prove that the following vectors are non-coplanar: hat i+2 hat j+3 hat k ,2\ hat i+ hat j+3 hat k\ a n d\ hat i+ hat j+ hat k

Prove that the following vectors are non coplanar: 3 hat i+ hat j- hat k ,2\ hat i- hat j+7 hat k\ a n d\ 7 hat i- hat j+23 hat k

Prove that the following vectors are coplanar: 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k\ a n d\ 3 hat i-4 hat j-4 hat k

Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\ 2 hat i+3 hat j- hat k\ a n d- hat i-2 hat j+2 hat k

Show that the points whose position vectors are as given below are collinear: 2 hat i+ hat j- hat k ,\ 3 hat i-2 hat j+ hat k\ a n d\ hat i+4 hat j-3 hat k 3 hat i-2 hat j+4 hat k ,\ hat i+ hat j+ hat k\ a n d-\ hat i+4 hat j-2 hat k

Prove that the following vectors are non-coplanar: 3 hat i+ hat j- hat k ,2 hat i- hat j+7 hat k and 7 hat i- hat j+23 hat k hat i+2 hat j+3 hat k ,2 hat i+ hat j+3 and hat i+ hat j+ hat k

Prove that the points having position vectors hat i+2 hat j+3 hat k ,\ 3 hat i+4 hat j+7 hat k ,\ -3 hat i-2 hat j-5 hat k are collinear.

Show that the four points having position vectors 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k ,2 hat i-5 hat j+10 hat k are coplanar.

Find the value of lambda for which the four points with position vectors - hat j- hat k ,4 hat i+5 hat j+lambda hat k ,3 hat i+9 hat j+4 hat k and 4 hat i+4 hat j+4 hat k are coplanar.

Show that the four points with position vectors 4 hat i+8 hat j+12 hat k ,\ 2 hat i+4\ hat j+6 hat k ,3 hat i+5\ hat j+4 hat k\ a n d\ 5 hat i+8\ hat j+5 hat k are coplanar.

RD SHARMA ENGLISH-THE PLANE -All Questions
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  2. Find the distance between the planes 2x-y+2z=4 and 6x-3y+6z=2.

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  3. Prove that the four points having position vectors are non-coplanar: ...

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  4. Find the equation of the plane mid parallel to the planes 2x-2y+z+3=0\...

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  5. Reduce the equation of line x-y+2z=5a d n3x+y+z=6 in symmetrical fo...

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  6. Find dy/dx if x=ay+b

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  7. If the line -> r=\ ( hat i-2 hat j+ hat k)+lambda(2 hat i+ hat j+2 ha...

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  8. Find the equation of the plane passing through the line of intersectio...

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  9. Find the equation of the plane passing through the intersection of the...

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  10. Find the equation of the plane passing through the intersection of the...

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  11. Find the equation of the plane passing through the point A(1,\ 2,\ 1) ...

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  12. Find an equation or the line that passes through the point P(2,\ 3,\ 1...

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  13. Find the angle between the line -> r=(2 hat i+3 hat j+9 hat k)+lambda...

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  14. Find the angle between the line (x-1)/1=(y-2)/(-1)=(z+1)/1 and the pla...

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  15. Find the angle between the line joining the points (3,\ -4,\ -2)a n d\...

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  16. The line vec r= hat i+lambda(2 hat i-m hat j-3 hat k) is parallel to ...

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  17. Find the vector equation of the line through the origin which is per...

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  18. Find the equation of the plane passes through the point (2,3,-4) and (...

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  19. Find the Cartesian equation of the plane passing through the points...

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  20. Find the vector and Cartesian equations of the line passing through (1...

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