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The vector equation of the plane through...

The vector equation of the plane through the point `(2, 1, -1)` and passing through the line of intersection of the plane `rcdot(hat(i)+3hat(j)-hat(k))=0 and rcdot(hat(j)2hat(k))=0,` is

A

`vecr cdot (hati + 9hatj + 11hatk)= 0`

B

`vecr cdot (hati + 9hatj + 11hatk)= 6`

C

`vecr cdot (hati - 3hatj - 13hatk)= 0`

D

`vecr cdot (2hati - 3hatj - 4hatk)= 0`

Text Solution

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The correct Answer is:
A
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The vector equation of the plane through the point hat(i)+2hat(j)-hat(k) and perpendicular to the line of intersection of the plane rcdot(3hat(i)-hat(j)+hat(k))=1 and rcdot(hat(i)+4hat(j)-2hat(k))=2 , is

Find the equation of the plane through the point 2 hat i+ hat j- hat k and passing through the line of intersection of the plane vec rdot(( hat i+3 hat j- hat k)=0\ a n d\ vec rdot(( hat j+2 hat k)=0.

A vector parallel to the line of intersection of the planes overset(to)( r) (3 hat(i) - hat(j) + hat(k) )=5 and overset(to) (r ) (hat(i) +4 hat(j) - 2 hat(k) )=3 is

Find the vector equation of the plane which contains the line of intersection of the plane vec rdot( hat i+2 hat j+3 hat k)-\ 4=0 and vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec rdot(5 hat i+3 hat j-\ 6 hat k)+8=0.

The vector equation of the plane through the point 2hat(i)-hat(j)-4hat(k) and parallel to the plane rcdot(4hat(i)-12hat(j)-3hat(k))-7=0 is

The equation of the plane passing through the point (1, 1, 0) and perpendicular to the line overset(to)( r) = 2 hat(i) + 3 hat(j) + 4 hat(k) + lambda ( 3 hat(i) + 4 hat(j) + 5hat(k) ) is

Find the vector equation of the plane passing through the intersection of the planes -> rdot( hat i+ hat j+ hat k)=6 and -> rdot(2 hat i+3 hat j+4 hat k)=-5 and the point (1, 1, 1).

Find the unit vector perpendicular the plane rcdot(2hat(i)+hat(j)+2hat(k))=5 .

Find the vector equation of the plane passing through the intersection of the planes -> rdot(2 hat i+2 hat j-3 hat k)=7, -> rdot(2 hat i+5 hat j+3 hat k)=9 and through the point (2, 1, 3).

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AAKASH INSTITUTE ENGLISH-THREE DIMENSIONAL GEOMETRY -ASSIGNMENT SECTION - B
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  2. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

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  3. Length of the perpendicular from origin to the plane passing through...

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  4. If the plane x- 3y +5z= d passes through the point (1, 2, 4), then the...

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  5. The plane x / 2 + y / 3 + z / 4 = 1 cuts the co-ordinate axes in A, B,...

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  6. The position vectors of points A and B are hati - hatj + 3hatk and 3h...

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  7. The vector equation of the plane through the point (2, 1, -1) and pass...

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  8. Find the vector equation of line passing through the point (1,2,-4)...

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  9. The line x + 2y - z - 3 = 0 = x + 3y - 2 - 4 is parallel to

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  10. The shortest distance between the lines 2x + y + z - 1 = 0 = 3x + y + ...

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  11. The lines x + y + z - 3 = 0 = 2x - y + 5z - 6 and x - y - z + 1 = 0 = ...

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  12. The line vecr= veca + lambda vecb will not meet the plane vecr cdot ...

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  13. The plane vecr cdot vecn = q will contain the line vecr = veca + lambd...

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  14. Two system of rectangular axes have the same origin. IF a plane cuts t...

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  15. Find the length of the perpendicular from the point (1,2,3) to the ...

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  16. A variable plane which remains at q constant distance 3p from the orig...

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  17. The planes 2x + 5y + 3z = 0, x-y+4z = 2 and7y-5z + 4 = 0

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  18. Let vecn be a unit vector perpendicular to the plane containing the ...

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  19. The coordinates of the point P on the line vecr=(hati+hatj+hatk)+lamda...

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  20. The projection of the line segment joining the Points (1, 2, 3) and ...

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