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Show that the lines vec r=3 hat i+2 ha...

Show that the lines ` vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k);` ` vec r=5 hat i-\ 2 hat j+mu(3 hat i+2 hat j+6 hat k)` ; are intersecting. Hence find their point of intersection.

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Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k) a n d vec r=(5 hat j-2 hat k)+mu(3 hat i+2 hat j+6 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 lines -> r=6 hat i+2 hat j+ hat k+lambda( hat i-2 hat j+2 hat k) and -> r=-4 hat i- hat k+mu(3 hat i-2 hat j-2 hat k) .

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)

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Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) are coplanar. Also, find the plane containing these two lines.

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.

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Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

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

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Using differentials, find the approximate value of sqrt(49. 5)

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  2. Using properties of determinants, prove the following: |[a^2 + 1,ab, ...

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  3. Show that the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 ha...

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  4. Find the particular solution of the differential equation satisfyin...

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  5. Find the general solution of the differential equation xlogx\ (dy)/...

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  6. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

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  7. If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

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  8. Find the value of k , for which f(x)={(sqrt(1+k x)-\ sqrt(1-k x))/(x)...

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  9. Two cards are drawn simultaneously (or successively without replace...

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  10. One kind of cake requires 200 g of flour and 25 g of fat, and anoth...

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  11. If vec a ,\ vec b ,\ vec c are three vectors such that vec a. v...

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  12. The probability that A hits a target is 1/3 and the probability tha...

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  13. Solve the following system of equations by matrix method. 3x-2y + 3z=...

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  14. Show that the lines (x+3)/(-3)=y-1/1=(z-5)/5;(x+1)/(-1)=(y-2)/2=(z-5)/...

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  15. Using integration, find the area of the region: {(x , y):9x^2+y^2l...

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  16. Consider the binary operations ** \: R\ xx\ R -> R and o\ : R\ xx\ R ...

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  17. Evaluate: intx^2\ cos^(-1)\ x\ dx

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  18. Evaluate : int1/(x+xlogx)\ dx

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  19. Find the area of the greatest rectangle that can be inscribed in an...

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  20. If the binary operation **, defined on Q, is defined as a**b=2a+b-a ...

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