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Show that the plane whose vector equatio...

Show that the plane whose vector equation is ` vec rdot( hat i+2 hat j= hat k)=3` contains the line whose vector equation is ` vec rdot( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot`

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Show that the plane whose vector equation is vec r*( hat i+2 hat j= hat k)=3 contains the line whose vector equation is vec r*( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot

Show that the plane whose vector equation is vec rdot( hat i+2 hat j- hat k)=1. and the line whose vector equation is vec r=(- hat i+ hat j+ hat k)+lambda(2 hat i+ hat j+4 hat k) are parallel. Also, find the distance between them.

Show that the line whose vector equation is vec rdot(2 hat i+5 hat j-7 hat k)+lambda( hat i+3 hat j+4 hat k) is parallel to the plane whose vector equation is vec rdot( hat i+ hat j- hat k)=7 . Also find the distance between them.

Find the shortest distance between the lines whose vector equations are: vec r=2 hat i- hat j- hat k+lambda(2 hat i-5 hat j+2 hat k)a n d\ , vec r= hat i+2 hat j+ hat k+ mu( hat i- hat j+ hat k)dot

Find the Cartesian form of equation of a plane whose vector equation is : vec rdot((- hat i+ hat j+2 hat k)=9

Find the shortest distance between the following pairs of line whose vector equation are: vec r=( hat i+2 hat j+3 hat k+lambda(2 hat i+3 hat j+4 hat k)a n d\ vec r=(2 hat i+4 hat j+5 hat k)+mu(3 hat i+4 hat j+5 hat k)

Find the Cartesian form of equation of a plane whose vector equation is : vec rdot((12 hat i-3 hat j+4 hat k)+5=0

Find the magnitude of vector vec a=(3 hat k+4 hat j)xx( hat i+ hat j- hat k)dot

Find the shortest distance between the following pairs of line whose vector equation are: vec r=3 hat i+8 hat j+3 hat k+lambda(3 hat i- hat j+ hat k)a n d\ vec r=-3 hat i-7 hat j+6 hat k+mu(-3 hat i+2 hat j+4 hat k)

Find the shortest distance between the lines whose vector equations are vec r= hat i+ hat j+lambda(2 hat i- hat j+ hat k) and vec r=2 hat i+ hat j- hat k+mu(3 hat i-5 hat j+2 hat k)dot

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
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  2. Find the equation of the plane which is parallel to the lines vec ...

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  3. Show that the plane whose vector equation is vec rdot( hat i+2 hat j=...

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  4. Find the vector equation of the following planes in Cartesian form:...

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  5. Show that the line of intersection of the planes vec rdot( hat i+2...

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  6. Find the equation of the plane passing through A(2,2,-1),B(3,4, 2) ...

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  7. Find the equation of the plane such that image of point (1,2,3) in ...

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  8. The foot of the perpendicular drawn from the origin to a plane is (...

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  9. Find the angel between the planes 2x+y-2z+3=0a n d vec rdot(6 hat i+...

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  10. Find the equation of the plane passing through (3,4,-1), which is p...

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  11. Find the distance of the point (-1,-5,-10) from the point of int...

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  12. Find the equation of the plane passing through the point (-1,3,2) an...

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  13. Find the angle between the line (x-1)/3=(y-1)/2=(z-1)/4 and the pla...

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  14. Find the distance between the line (x+1)/(-3)=(y-3)/2=(z-2)/1 and t...

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  15. The extremities of a diameter of a sphere lie on the positive y- an...

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  16. A plane passes through a fixed point (a ,b ,c)dot Show that the loc...

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  17. Find the radius of the circular section of the sphere | vec r|=5 by...

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  18. A point P(x ,y ,z) is such that 3P A=2P B , where Aa n dB are the p...

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  19. Find the shortest distance between lines vec r=( hat i+2 hat j+ hat...

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  20. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/4a ...

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