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Find the equations of the line through t...

Find the equations of the line through the point ( 1 , -2, -3) and parallel to the vector `2 hat i + 3 hat j + 4 hat k ` in Cartesian form.

A

The equation of the plane through the given point is `3x-4y+7z+13=0`.

B

perpendicular distance of plane from origin `(1)/(sqrt(74))`.

C

perpendicular distance of plane from origin `(13)/(sqrt(74))`.

D

perpendicular distance of plane from origin `(21)/(sqrt(74))`.

Text Solution

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The correct Answer is:
(a,c)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (More Than One Correct Option Type Questions)
  1. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve x^2+y^2=r...

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  2. A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(...

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  3. Find the equations of the line through the point ( 1 , -2, -3) and par...

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  4. A plane passes through a fixed point (a, b, c) and direction ratios of...

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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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  20. Find dy/dx if y=log(logx)

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