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Find the line of intersection of the pla...

Find the line of intersection of the planes `vecr.(3hati-hatj+hatk)=1 and vecr.(hati+4hatj-2hatk)=2`

A

`2hati+7hatj+13hatk`

B

`-2hati-7hatj+13hatk`

C

`2hati+7hatj+13hatk`

D

`-2hati+7hatj+13hatk`

Text Solution

Verified by Experts

The correct Answer is:
D
We know that the line of intersection of the planes `vecr.vecn_(1)=d_(1)` and `vecr.n_(2)=d_(2)` is parallel to `vecn_(1)xxvecn_(2)`.
Hence `vecn_(1)-3hati-hatj+hatk` and `vecn_(2)+4hatj-2hatk`
`:.` Required vector `=vecn_(1)xxvecn_(2)=|(hati,hatj,hatk),(3,-1,1),(1,4,-2)|=-2hati+7hatj+13hatk`
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Show that the line of intersection of the planes vecr*(hati+2hatj+3hatk)=0 and vecr*(3hati+2hatj+hatk)=0 is equally inclined to hati and hatk . Also find the angleit makes with hatj .

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OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Section I - Solved Mcqs
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  2. Equations of the line passing through (1,1,1) and perpendicular to th...

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  4. Given the line L: (x-1)/(3) = (y+1)/(2) = (z +3)/(1) and the plane pi...

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  5. The equation of the plane containing the line vecr = hati + hatj + lam...

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  6. The ratio in which the plane vecr.(veci-2 vecj+3veck)=17 divides the l...

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  7. The sine of the angle between the line (x-2)/(3) = (y-3)/(4) = (z-4)/(...

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  8. If the plane x/2+y/3+z/6=1 cuts the axes of coordinates at points, A ,...

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  9. Let the pairs veca, vecb and vecc vecd each determine a plane. Then th...

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

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

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

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

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

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

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

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

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

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