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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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Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to x axis.

Find the vector equation of the plane passing through the intersection of the two planes vecr(hati+hatj+hatk)=6 and vecr(2hati+3hatj+4hatk)=-5 and through the point (1,1,1)

Find the equation of the plane which contains the line of intersection of the planes vecr.(hati+2hatj+3hatk)-4=0 and vecr.(2hati+hatj-hatk)+5=0 and which is perpendicular to the plane vecr.(5hati+3hatj-6hatk)+8=0

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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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 vec r=(1+lambda-mu) hat i+(2-l...

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

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  4. Let L1 be the line vec r1=2 hat i+ hat j- hat k+lambda(i+1 hat k) and...

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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 perpendicul...

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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 o the foot of the perpendicular drawn from the orig...

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  15. about to only mathematics

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

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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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