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Equation of any plane containing the line `(x-x_1)/(a)=(y-y_1)/(b)=(z-z_1)/(c)` is `A(x-x_1)+B(y-y_1)+C(z-z_1)=0` then pick correct alternatives

A

`(A)/(a)=(B)/(b)=(C)/(c)` is true for the line to be perpendicular to the plane.

B

`A(a+3)+B(b-1)+C(c-2)=0`

C

`2aA+3bB+4cC=0`

D

`Aa+Bb+Cc=0`

Text Solution

Verified by Experts

The correct Answer is:
(a, d)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (More Than One Correct Option Type Questions)
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  3. Equation of any plane containing the line (x-x1)/(a)=(y-y1)/(b)=(z-z1)...

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

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  6. Consider the plane through (2, 3, -1) and at right angles to the vecto...

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  7. A plane passes through a fixed point (a, b, c) and cuts the axes in A,...

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  8. Let A be vector parallel to line of intersection of planes P1 and P2. ...

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  9. Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2, then

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  10. If p1, p2, p3 denote the perpendicular distance of the plane 2x-3y+4z+...

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  11. A line segment has length 63 and direction ratios are 3, -26. The comp...

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

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

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

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  15. A rod of length 2units whose one end is (1, 0, -1) and other end touch...

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  16. Consider the planes p1: 2x+y+z+4=0, p2: y-z+4=0 and p3: 3x+2y+z+8=0 ...

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  17. The volume of a tetrahedron prism ABCA1B1C1 is equal to 3. Find the co...

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  18. If the plane passing through the origin and parallel to the line (x-1)...

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

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

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