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Let a1x+b1y+c1z+d1=0 and a2x+b2y+c2z+d2=...

Let `a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2y+c_2z+d_2=0 ` be two planes, where `d_1, d_2gt0`. Then, origin lies in acute angle, If `a_1a_2+b_1b_2+c_1c_2lt0` and origin lies in obtuse angle if `a_1a_2+b_1b_2+c_1c_2gt0`.
Further point `(x_1, y_1, z_1)` and origin both lie either in acute angle or in obtuse angle. If ( `a_1x_1+b_1y_1+c_1z_1+d_1)(a_2x_1+b_2y_1+c_2z_1+d_2)gt0`.
one of `(x_1, y_1, z_1)` and origin in lie in acute and the other in obtuse angle,If ( `a_1x_1+b_1y_1+c_1z_1+d_1)(a_2x_1+b_2y_1+c_2z_1+d_2)lt0`
Q. Given that planes `2x+3y-4z+7=0 and x-2y+3z-5=0`. If a point `P(1, -2, 3),` then

A

O and P both lie in acute angle between the planes

B

O and P both lies in obtuse angle

C

O lies in acute angle, P lies in obtuse angle

D

O lies in obtuse angle, P lies in acute angle

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The correct Answer is:
B
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Consider a pyramid OPQRS located in the first octant (xge0, yge0, zge0...

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  3. Let P be the image of the point (3, 1, 7) with respect to the plane x...

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  4. From a point P(lambda, lambda, lambda), perpendicular PQ and PR are dr...

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  5. Two lines L(1) : x=5, (y)/(3-alpha)=(z)/(-2) and L(2) : x=alpha, (y)/(...

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  6. A line l passing through the origin is perpendicular to the lines 1:...

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  7. Perpendicular are drawn from points on the line (x+2)/(2)=(y+1)/(-1)=...

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  8. If the straight lines (x-1)/(2)=(y+1)/(k)=(z)/(2) and (z+1)/(5)=(y+1)/...

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  9. If the distance between the plane Ax-2y+z=d and the plane containing ...

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  10. Read the following passage and answer the questions. Consider the line...

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  11. Read the following passage and answer the questions. Consider the line...

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  12. Read the following passage and answer the questions. Consider the line...

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  13. Consider three planes P(1):x-y+z=1 P(2):x+y-z=-1 and " "P...

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  14. Consider the planes 3x-6y-2z=15a n d2x+y-2z=5. Statement 1:The parame...

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  15. If the image of the point P(1,-2,3) in the plane, 2x+3y-4z+22=0 measur...

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  16. The distance of the point (1, 3, -7) from the plane passing through th...

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  17. The distance of the point (1,-5,""9) from the plane x-y+z=5 measured a...

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  18. If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the place, l x+m y-z=9...

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  19. The disatance of the point (1, 0, 2) from the point of intersection of...

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  20. The equation of the plane containing the line 2x-5y+z=3, x+y+4z=5 and ...

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  21. The angle between the lines whose direction cosines satisfy the equ...

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