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A set of D.R of the line vecr=(hati+hatj...

A set of D.R of the line
`vecr=(hati+hatj+hatk)+1(2hati+3hatj+6hatk)`are

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Find the point of intersection of the line : vecr=(hati+2hatj+3hatk)+lambda(2hati+hatj+2hatk) and the plane vecr*(2hati-6hatj+3hatk)+5=0 .

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

Find the distance of the point with position vector -hati-5hatj-10hatk from the point of intersection of the line vecr=(2hati-hatj+2hatk)+lambda(3hati+4hatj+12hatk) and the plane vecr*(hati-hatj+hatk)=5 .

Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the shortest distance between the lines vecr = (hati + 2hatj+hatk) + lambda(hati-hatj+hatk) and vecr = 2hati - hatj-hatk + mu(2hati+hatj+2hatk)

Find the angle between the line : vecr=(hati-hatj+hatk)+lambda(2hati-hatj+3hatk) and the plane vecr*(2hati+hatj-hatk)=4 . Also find whether the line is parallel to the plane or not.

Find the equation of the line passing through the point (1,2,-3) and perpendicular to the lines : vecr=(2hati-hatj-hatk)+lambda(2hati-hatj-3hatk) and vecr=(3hati-hatj-2hatk)+mu(hati+hatj+hatk)

Find the equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the equation of the line passing through the point (2, -1, 3) and perpendicular to the lines : vecr=(hati-hatj+hatk)+lambda(2hati+hatj-3hatk) and vecr=(hati+hatj-hatk)+mu(hati+hatj+hatk)

Find the equation of the line passing through the point (1,-2,3) and perpendicular to the lines : vecr=(hati-2hatj+hatk)+lambda(hati+hatj+hatk) and vecr=(hati-hatj+2hatk)+mu(3hati-2hatj-5hatk)

PRADEEP PUBLICATION-MODEL PAPER (2)-EXERCISE
  1. Let A={a,b,c} and R={(a,a),(b,b),(a,b),(b,c),(a,c)} be a relation on A...

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  2. Evaluate underset(-1)overset(1)int log((x^2+x+1)/(x^2-x+1))dx.

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  3. A set of D.R of the line vecr=(hati+hatj+hatk)+1(2hati+3hatj+6hatk)are

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  4. Observe the following pattern : .

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  5. Show that 1/x^2 is an integrating factor for the differential equation...

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  6. Let f(x)={(xsin(1/x), x ne 0),(k, x=0):} find k if f is continuous at ...

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  7. Evaluate underset(xrarr0)Lt [cosx] if it exists. Here [] denotes the g...

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  8. If y=sqrt(x+1)+sqrt(x-1), prove that sqrt(x^2-1)(dy)/(dx)=1/2y.

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  9. Evaluate underset(-1)overset1 int 1/(1+e^x)dx.

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  10. Find the equation of the plane given that the foot of perpendicular d...

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  11. Find the transpose of {:[(a,b),(c,d)]

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  12. Evaluate: underset0overset(pi//2)int log(sinx)dx

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  13. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  14. Let A=Set of all real numbes except 1. Let * be defined as a+b-ab for...

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  15. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

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  16. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

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  17. Prove that cot^-1 7 + cot^-1 8 + cot^-1 18 = cot^-1 3

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  18. Solve the following equations sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1

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  19. Solve the following equations 5x-7y+z=11, 6x-8y-z=15, 3x+2y-6z=7 by Cr...

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  20. Find dy/dx if x^y + y^x = a^b

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