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The cartesian eqaution of the plane r=(1...

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

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For what value of lambda are the vectors lambda hat(i)+(1 + lambda) hat(j) + (1 + 2 lambda) hat( k) and (1-lambda) hat(i)+lambda hat(j) + 2 hat(k) perpendicular ?

Find the vector equation of the following planes in non- parametric form: (i) vec r=(lambda-2 mu)hat i+(3-mu)hat j+(2 lambda=mu)hat k.(ii)vec r=(2hat i+2hat j-hat k)+lambda(hat i+2hat j+3hat k)+mu(5hat i-2hat j+7hat 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

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Find the point of intersection of the line : vec(r) = (hat(i) + 2 hat(j) + 3 hat(k) ) + lambda (2 hat(i) + hat(j) + 2 hat(k)) and the plane vec(r). (2 hat(i) - 6 hat(j) + 3 hat(k) ) + 5 = 0.

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Questions Asked In Previous 13 Years Exam)
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  4. From a point P(lambda, lambda, lambda), perpendicular PQ and PR are dr...

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  6. A line l passing through the origin is perpendicular to the lines 1:...

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  7. Perpendicular are drawn from points on the line (x+2)/(2)=(y+1)/(-1)=...

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  8. If the straight lines (x-1)/(2)=(y+1)/(k)=(z)/(2) and (z+1)/(5)=(y+1)/...

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  9. If the distance between the plane Ax-2y+z=d and the plane containing ...

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  12. Read the following passage and answer the questions. Consider the line...

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  13. Consider three planes P(1):x-y+z=1 P(2):x+y-z=-1 and " "P...

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  14. Consider the planes 3x-6y-2z=15a n d2x+y-2z=5. Statement 1:The parame...

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  15. If the image of the point P(1,-2,3) in the plane, 2x+3y-4z+22=0 measur...

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  16. The distance of the point (1, 3, -7) from the plane passing through th...

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  17. The distance of the point (1,-5,""9) from the plane x-y+z=5 measured a...

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  18. If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the place, l x+m y-z=9...

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  19. The disatance of the point (1, 0, 2) from the point of intersection of...

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  20. The equation of the plane containing the line 2x-5y+z=3, x+y+4z=5 and ...

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  21. The angle between the lines whose direction cosines satisfy the equ...

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