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The equation of the plane containing the...

The equation of the plane containing the lines `vecr = vec a _(1) + lamda vecb and = vec a _(2) + mu hat b ` is :

A

`[(vecr, veca, vecb)]=0`

B

`[(vecr,veca,vecb)]=veca.vecb`

C

`[(veca,vecb,veca)]=veca.vecb`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
The required plane passes through the points having position vectors `veca` and `vecb`. It is perpendicular to `vecaxxvecb`.
So theequation of the plane is
`(vecr-veca).(vecaxxvecb)=0impliesvecr.(vecaxxvecb)=veca.(vecaxxvecb)implies[(vecr,veca,vecb)]=0`
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OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Section I - Solved Mcqs
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  2. Let the pairs veca, vecb and vecc vecd each determine a plane. Then th...

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  3. The equation of the plane containing the lines vecr = vec a (1) + lam...

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  4. The points A(2-x,2,2), B(2,2-y,2), C(2,2,2-z) and D(1,1,1) are coplana...

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  5. Find the vector equation of the plane in which the lines vecr=hati+ha...

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  6. The equation of the plane which contains the origin and the line of in...

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  7. The length of the perpendicular from the origin to the plane passing t...

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  8. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

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  9. The equation of the plane which bisects the line joining (2, 3, 4) and...

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  10. Distance of the point P(vecp) from the line vecr=veca+lamdavecb is ...

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  11. Distance of the point P(x2, y2, z2) from the line (x-x1)/l=(y-y1)/m=(z...

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  12. If veca,vecb and vecc are three non-coplanar vectors then the length o...

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  13. If P(0, 1, 0) and Q(0, 0 1) are two points, then the projection of PQ ...

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  14. A plane passes through the point (1, 1, 1). If b, c, a are the direc...

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  15. If the foot of the perpendicular from O(0,0,0) to a plane is P(1,2,2)....

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  16. The equation of the plane through the point (1,2,3) and parallel to th...

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  17. The straight line (x-3)/3=(y-2)/1=(z-1)/0 is Parallel to x-axis Parall...

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  18. The direction ratios o f a normal to the plane through (1,0,0) and (0,...

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  19. Find the equation of a plane which passes through the point (3, 2, 0...

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  20. If the lines (x-1)/2=(y+1)/3=(z-1)/4a n d(x-3)/1=(y-k)/2=z/1 intersect...

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