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A plane makes intercepts OA, OB and OC w...

A plane makes intercepts OA, OB and OC whose measurements are b and c on the OX, OY and OZ axes. The area of `triangle ABC` is

A

`(1)/(2)(ab+bc+ac)`

B

`(1)/(2)abc(a+b+c)`

C

`(1)/(2)(a^2b^2+b^2c^2+c^2a^2)^(1/(2)`

D

`(1)/(2)(a+b+c)^2`

Text Solution

Verified by Experts

The correct Answer is:
(c)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. Differentiate x^5 with respect to x.

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  2. Let P(3, 2, 6) be a point in space and Q be a point on line vecr= (hat...

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  3. A plane makes intercepts OA, OB and OC whose measurements are b and c ...

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  4. The radius of the circle in which the sphere x^(2)=y^(2)+z^(2)+2z-2y-4...

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  5. Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection...

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  6. The coordinates of the point P on the line vec r=( hat i+ hat j+ ha...

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  7. Find 3-dimensional vectors vec v1,vec v2,vec v3 satisfying vec v1* ve...

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  8. The position vectors of points a and b are hat(i)-hat(j)+3hat(k) and 3...

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  9. A, B, C and D are four points in space. Using vector methods, prove th...

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  10. Find the value of x Equation is x+2=9

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  11. If the three planes rcdotn1=p1, rcdotn2=p2 and rcdotn3=p3 have a commo...

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  12. A pentagon is formed by cutting a triangular corner from a rectangular...

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  13. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

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  14. A plane 2x+3y+5z=1 has a point P which is at minimum distance from lin...

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  15. Evaluate int x^5 dx

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  16. A cube C={(x, y, z)|o le x, y, zle1} is cut by a sharp knife along the...

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  17. A ray of light is sent through the point P(1,2,3) and is reflected on ...

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  18. Find dy/dx if 2x-3sinx=2y

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  19. The shortest distance between any two opposite edges of the tetrahedro...

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  20. The angle between the pair of planes represented by equation 2x^(2)-2y...

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