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Find the shortest distance between the following lines: ` vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)` and ` vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)`

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Find the angel between the following pair of lines: vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)a n d vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k) x/2=y/2=z/1a n d(x-5)/4=(y-2)/1=(z-3)/8

Find the angle between the lines vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k) and vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)dot

Find the shortest distance between the lines: vec r=6 hat i+2 hat j+2 hat k+lambda\ ( hat i-2 hat j+2 hat k) and vec r=-4 hat i- hat k+mu\ (3 hat i-\ 2 hat j-\ 2 hat k)

Find the angle between the lines vec r=(2 hat i-5 hat j+ hat k)+lambda(3 hat i+2 hat j+6 hat k)a n d\ vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)dot

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

Find the shortest distance between the lines: vec r=6 hat i+2 hat j+2 hat k+lambda( hat i-2 hat j+2 hat k)a n d\ vec r=-4 hat i- hat k+mu(3 hat i-2 hat j-2 hat k)dot

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

Find the angle between the following pairs of lines:(i) -> r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k) and -> r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k) (ii) -> r=3 hat i+ hat j-2 hat k+lambda( hat i- hat j-2 hat k) and -

Find the shortest distance between the lines: vec r= hat i+2 hat j+3 hat k+lambda( hat i-3 hat j+2 hat k)a n d\ vec r=4 hat i+5 hat j+6 hat k+mu(2 hat i+3 hat j+ hat k)dot

Determine the shortest distance between the pair of lines : vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d\ vec r=(2 hat i- hat k)+mu(2 hat i+2 hat k)dot

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. If y=A e^(m x)+B e^(n x), show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y...

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  2. Find : int(x+3)/(sqrt(5-4x+x^2))dx

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  3. Find the shortest distance between the following lines: vec r=2 hat i...

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  4. For what value of lambda the function defined by f(x)={lambda(x^2+2),i...

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  5. If x=a e^t(sint+cost) and y=a e^t(sint-cost), prove that (dy)/(dx)=(x+...

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  6. Evaluate : int0^(pi/4)log(1+tanx)dxdot

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  7. Find : intx/((x-1)^2(x+2))dx

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  8. A point on the hypotenuse of a right triangle is at distances a and b ...

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  9. Evaluate: int[x+2]/[2x^2+6x+5]dx

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  10. Write the order of the differential equation 1+((dy)/(dx))^2=7\ ((d^2y...

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  11. Two schools A and B decided to award prizes to their students for thre...

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  12. If A=(1 2 3-1)a n dB=(1 3-1 1), write the value of |A B| .

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  13. Write the differential equation obtained by eliminating the arbitrary ...

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  14. If vec a and vec b are unit Vectors, then what is the angle betwe...

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  15. If a line makes angles alpha,beta,gamma with the positive direction of...

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  16. Find a Vector in the direction of vec a= hat i-2 hat j that has magni...

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  17. Let A = R × R and * be the binary operation on A defined by (a, b) *...

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  18. Find the inverse of the matrix A=[1 3 3 1 4 3 1 3 4]

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  19. If [2x3][1 2-3 0][x3]=O , find x

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  20. Find the equation of the plane through the line of intersection of the...

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