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A unit vector parallel to the intersecti...

A unit vector parallel to the intersection of the planes `vecr.(hati-hatj+hatk)=5 andvecr.(2hati+hatj-3hatk)=4` is

A

`(2hati+5hatj-3hatk)/(sqrt38)`

B

`(2hati-5hatj+3hatk)/(sqrt38)`

C

`(-2hati-5hatj-3hatk)/(sqrt38)`

D

`(-2hati+5hatj-3hatk)/(sqrt38)`

Text Solution

Verified by Experts

The correct Answer is:
C
`hata=pm(vecn_(1)xxvecc_(2))/(|vecn_(1)xxvec n_(2)|)=pm(2hati+5hatj+3hatk)/(sqrt38)`
(where `vecn_(1)andvecn_(2)` are normal to the planes)
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. The distance of point A(-2,3,1) from the line P Q through P(-3,5,2), w...

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  2. The Cartesian equation of the plane vecr=(1+lamda-mu)hati+(2-lamda)hat...

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  3. A unit vector parallel to the intersection of the planes vecr.(hati-ha...

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  4. Let L(1) be the line vecr(1)=2hati+hatj-hatk+lamda(hati+2hatk) and let...

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  5. For the line (x-1)/1=(y-2)/2=(z-3)/3, which one of the following is...

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  6. Find the value of m for which thestraight line 3x-2y+z+3=0=4x=3y+4z+1 ...

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  7. The intercept made by the plane vec rdot vec n=q on the x-axis is ...

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  8. Equation of a line in the plane pi-=2x-y+z-4=0 which is perpendicula...

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  9. If the foot of the perpendicular from the origin to plane is P(a ,b...

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  10. The equation of the plane which passes through the point of interse...

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  11. Let A( vec a)a n dB( vec b) be points on two skew lines vec r= vec a+...

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  12. Let A(1,1,1),B(23,5)a n dC(-1,0,2) be three points, then equation of a...

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  13. The point on the line (x-2)/1=(y+3)/(-2)=(z+5)/(-2) at a distance of 6...

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  14. The coordinates of the foot of the perpendicular drawn from the orig...

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  15. If P1:vec r.vecn1-d1=0 P2:vec r.vec n2-d2=0 and P3:vec r.vecn3-d3=0 ar...

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  16. The length of projection of the line segment joining the points (1,0...

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  17. The number of planes that are equidistant from four non-coplanar po...

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

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  19. A plane passing through (1,1,1) cuts positive direction of coordinates...

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  20. If lines x=y=za n dx=y/2=z/3 and third line passing through (1,1,1) fo...

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