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The points A(4, 5, 10), B(2, 3, 4) and C...

The points `A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1)` are three vertices of a parallelogram ABCD. Find the vector equations of side AB and BC and also find the coordinates of point D .

A

Vector equation of AB is `2i+3j+4k+lambda(i+j+3k)`

B

Cartesian equation of BC is `(x-2)/(1)=(y-3)/(1)=(z-4)/(-5)`

C

Coordinate of D are `(3, 4,5)`

D

ABCD is a rectangle.

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(a,b, c)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (More Than One Correct Option Type Questions)
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  5. Let A be vector parallel to line of intersection of planes P1 and P2. ...

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  6. Find the angle between the planes 2x+y+z-1=0 and 3x+y+2z-2=0,

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  7. Find the direction ratios of this plane 2x-3y+4z+2=0

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  8. A line segment has length 63 and direction ratios are 3,-2 and 6. The ...

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  9. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

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  10. The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices ...

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  11. The lines x=y=z meets the plane x+y+z=1 at the point P and the sphere ...

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  12. Evaluate int 4x^5 dx

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  13. Consider the planes 2x+y+z+4=0, and y-z+4=0 Find the angle between the...

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  14. The volume of a right triangular prism ABCA(1)B(1)C(1) is equal to 3 c...

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  15. Find the multiplication of 34×0

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  16. Let OABC be a regular tetrahedron with side length unity, then its vol...

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  17. The OABC is a tetrahedron such that OA^2+BC^2=OB^2+CA^2=OC^2+AB^2,then

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  18. If the line (x)/(1)=(y)/(2)=(z)/(3) then convert this in a vector form

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  19. Let PM be the perpendicular form the point P(1,2,3) to the x-y plnae. ...

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