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Reduce the equations overset(-)r . (3ha...

Reduce the equations ` overset(-)r . (3hati +4hatj +12 hatk ) =8` to normal form.

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The correct Answer is:
`overset(-)r =( 3hati +4hatj+12 hatk ) /(13) =(8)/(13)`
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Reduce the equation barr*(3hati - 4hatj + 12hatk) = 3 to the normal form and hence find the length of perpendicular from the origin to the plane.

Find the shortest distance between the lines whose vector equations are : vec(r) = (hati + 2 hatj + 3 hatk ) + lambda (hati -3 hatj + 2 hatk) and vec(r) = 4 hati + 5 hatj + 6 hatk + mu (2 hati + 3 hatj + hatk) .

Find the shortest distance between the lines l_(1)and l_(1) whose vector equations are vecr=(hati+hatj) + lambda (3hati + 4hatj - 2hatk) …(i) and vecr=(2hati+3hatj) + mu (6hati + 8hatj - 4hatk) …(ii)

Find the vector equations of the line passing through the point having positions vector -hati -hatj +2hatk and parallel to the line overset(-) r = ( hati+ 2hatj + 3hatk ) +mu (3hati + 2hatj +hatk) , mu is a parameter .

Verify if the point having positions vector 4 hati-11 hatj +2 hatk lies on the line overset (-)r =( 6 hati -4 hatj +5hatk ) +mu (2hati +7hatj +3hatk )

Find the equation of the plane , which contains the line of intersection of the planes : vec(r). (hati + 2 hatj + 3 hatk) -4 = 0 and vec(r). (2 hati + hatj + hatk) + 5 = 0 and which is perpendicular to the plane : vec(r) . (5 hati + 3 hatj - 6 hatk) ) + 8 = 0 .

Equation of the plane is barr*(3hati - 4hatj + 12hatk) = 8 Find the length of the perpendicular from the origin to the plane.

Find a unit vector in the diection of the vector. (i) (3hati + 4hatj - 5hatk) , (ii) (3hati - 2hatj + 6hatk) (iii) (hati + hatk) , (iv) (2hati + hatj + 2hatk)

Equation of a plane is bar(r).(3hati - 4hatj+12hatk)=8 . Find the length of the perpendicualr from the origin to the plane.

Find the shortest distance between the lines: (i) vec(r) = 3 hati + 8 hat(j) + 3 hatk + lambda (3 hati - hatj + hatk) and vec(r) = - 3 hat(i) - 7 hatj + 6 hatk + mu (-3 hati + 2 hatj + 4 hatk ) (ii) ( hati - hatj + 2 hatk) + lambda ( -2 hati + hatj + 3 hatk ) and (2 hati + 3 hatj - hatk) + mu (3 hati - 2 hatj + 2 hatk). (iii) vec(r) = (hati + 2 hatj + 3 hatk) + lambda ( hati - 3 hatj + 2 hatk ) and vec(r) = (4 hati + 5 hatj + 6 hatk) + mu (2 hati + 3 hatj + hatk) .

NAVNEET PUBLICATION - MAHARASHTRA BOARD-QUESTION BANK 2021-LINE AND PLANE
  1. Find the directions cosines of the normal to the plane overset (-)r ....

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  2. If the normal to the plane has directions ratios 2,-1,2 and it's perpe...

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  3. Reduce the equations overset(-)r . (3hati +4hatj +12 hatk ) =8 to nor...

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  4. If the normal to the plane has directions ratios 2,-1,2 and it's perpe...

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  5. Find the perpendicular distance of origin from of the plane 6x-2y+3z ...

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  6. Find the acute angle between the lines x=y: z=0 and x=0z=0

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  7. Find Cartesian equations of the line passing through the point A(2,1,-...

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  8. Find the vector equations of the line passing through the point having...

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  9. Find the Cartesian equations of the line passing through (-1,-1,2) and...

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  10. Find the Cartesian equations of the plane passing through A(7,8,6) and...

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  11. Find the coordinates of the foot of perpendicular from of the origin t...

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  12. Find the vector equations of a plane at a distance 6 units from the or...

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  13. The cartesian equation of the plane passing through the points (1 ,1,2...

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  14. Find the acute angle between the lines (x-1)/(1)= (y-2)/(-1) =(z-3)/(...

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  15. Find the distance between the parallel lines (x)/(2) =(y)/(-1) =(z)/...

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  16. Find the equations of the plane passing through the point (7,8,6) and ...

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  17. Fiind m, if the lines (1-x)/(3)= ( 7y-14)/(2m ) = (z-3) /(2) and ( 7-7...

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  18. Show that the lines ( x+1)/(-10) = ( y + 3)/(-1) = ( z - 4) / (1) "an...

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  19. A(-2,3,4), B(1,1,2),C(4,-1,0) are three points. Find the Cartesian equ...

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  20. The vector equation of a line passing through the point hati + 2hatj +...

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