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The Cartesian equation of the plane ...

The Cartesian equation of the plane ` vec r=(1+lambda-mu) hat i+(2-lambda) hat j+(3-2lambda+2mu) hat k` is a. `2x+y=5` b. `2x-y=5` c. `2x+z=5` d. `2x-z=5`

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Find the vector equation of the following plane in non-parametric form: vec r=(lambda-2mu) hat i+(3-mu) hat j+(2lambda+mu) hat k .

Find the vector equation of the following planes in non parametric form: -> r=(lambda-2mu) hat i+(3-mu) hat j+(2lambda+mu) hat k

Find the shortest distance between the lines vec r=(1-lambda) hat i+(lambda-2) hat j+(3-2lambda) hat k and vec r=(mu+1) hat i+(2mu+1) hat kdot

Find the shortest distance between the following pairs of line whose vector equation are: vec r=(lambda-1) hat i+(lambda+1) hat j-(1+lambda) hat k\ a n d\ vec r=(1-mu) hat i+(2mu-1) hat j+(mu+2) hat k .

Find the vector and Cartesian equations of the plane containing the two lines vec r=2 hat i+ hat j-3 hat k+lambda( hat i+2 hat j+5 hat k)a n d , vec r=3 hat i+3 hat j+2 hat k+mu(3 hat i-2 hat j+ 5hat k)

Find lambda and mu if (2 hat i+6 hat j+27 hat k)xx( hat i+lambda hat j+mu hat k)= vec 0 .

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

Find the vector equation of the following planes in Cartesian form: vec r= hat i- hat j+lambda( hat i+ hat j+ hat k)+mu( hat i-2 hat j+3 hat k)dot

Find the angel between the planes 2x+y-2z+3=0a n d vec rdot(6 hat i+3 hat j+2 hat k)=5.

The number of distinct real values of lambda , for which the vectors -lambda^2 hat i+ hat j+k , hat i-lambda^2 hat j+ hat ka n d hat i+ hat j-lambda^2 hat k are coplanar is a. zero b. one c. two d. three

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Let L1 be the line vec r1=2 hat i+ hat j- hat k+lambda(hat i+2 hat k)...

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  2. The distance of point A(-2,3,1) from the line P Q through P(-3,5,2), w...

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  3. The Cartesian equation of the plane vec r=(1+lambda-mu) hat i+(2-l...

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  4. Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda...

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  5. The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambd...

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  6. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

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  7. Statement 1: there exists a unique sphere which passes through the ...

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  8. Statement 1: There exist two points on the (x-1)/1=y/(-1)=(z+2)/2 w...

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  9. Statement 1: The shortest distance between the lines x/(-3)=(y-1)/1=(z...

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  10. Find the number of sphere of radius r touching the coordinate axes...

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  11. Find the distance of the z-axis from the image of the point M(2-3,3...

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  12. A line with direction cosines proportional to 1,-5, a n d-2 meets li...

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  13. If the planes vec rdot( hat i+ hat j+ hat k)=q1, vec rdot( hat i+2a h...

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  14. The equation of a line passing through the point vec a parallel to ...

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  15. A straight line L on the xy-plane bisects the angle between O Xa n dO ...

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  16. Statement 1: Vector vec c=5 hat i+7 hat j+2 hat k is along the bisect...

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  17. The equation of the line x+y+z-1=0, 4x+y-2z+2=0 written in the symmetr...

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  18. The equation of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3)a n...

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  19. Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a...

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  20. Statement 1: Line (x-1)/1=(y-0)/2=(z2)/(-1) lies in the plane 2x-3y-4z...

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