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Find the vector equation of the plane passing through the points `(2,\ 1,\ -1)\ a n d\ (-1,\ 3,\ 4)` and perpendicular to the plane `x\ -\ 2y+4z=10` . Also show that the plane thus obtained contains the line ` vec r=- hat i+3 hat j+4 hat k+lambda\ (3 hat i-2 hat j-\ 5 hat k)dot`

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Find the vector equation of the plane passing through the points (3, 4, 2) and (7, 0, 6) and perpendicular to the plane 2x-5y-15=0. Also, show that the plane thus obtained contains the line vec r= hat i+3 hat j-2 hat k+lambda( hat i- hat j+ hat k)dot

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane -> r(dot( hat i+2 hat j-5 hat k))=9.

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vec r.( hat i+2 hat j-5 hat k)+9=0 .

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

Find the vector equation of a line passing through 3 hat i-5 hat j+7 hat k and perpendicular to the plane 3x-4y+5z=8.

Find the vector equation of the plane passing through the points 3 hat i+4 hat j+2 hat k ,2 hat i-2 hat j- hat ka n d7 hat i+6 hat kdot

Find the vector equation of the line passing through the point (1,2,3) and parallel to the planes vec rdot( hat i- hat j+2 hat k)=5 and vec rdot(3 hat i+ hat j+ hat k)=6.

Write the vector equation of the line passing through (1,2,3) and perpendicular to the plane vec r.( hat i+2 hat j-5 hat k)+9=0.

Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

Find the angle between the plane: vec rdot((2 hat i-3 hat j+4 hat k)=1\ a n d\ vec rdot((- hat i+ hat j)=4 .

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Show that the differential equation ((x-y)dy)/(dx)=x+2y , is homoge...

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  2. In a certain college, 4% of boys and 1% of girls are taller than 1....

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  3. Find the vector equation of the plane passing through the points (2,...

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  4. Evaluate the following int0^(3/2)|xcospix\ |\ dxdot

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  5. Prove that the area in the first quadrant enclosed by the axis, the ...

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  6. Show that the altitude of the right circular cone of maximum volume ...

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  7. Solve for x: tan^(-1)3x+tan^(-1)2x=pi/4

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  8. Prove that: sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2

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  9. If vecalpha=3 hat i+4 hat j+5 hat k and vecbeta=2 hat i+ hat j-\ 4 h...

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  10. Evaluate : int(cosx)/((2+sinx)\ (3+4sinx) dx

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  11. If [[1,2],[3,4]] [[3,1],[2,5]]=[[7,11],[k,23]], then write the value o...

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  12. Find the particular solution of the differential equation. (dy)/(dx...

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  13. Show that f\ : NvecN ,\ given by f(x)={x+1, if\ x\ i s\ od d \ \ x-...

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  14. Evaluate : int(logx)/x\ dxdot

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  15. What is the value of the determinant |(0,2,0),(2,3,4),(4,5,6)|?

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  16. What is the degree of the following differential equation? 5x\ ((d...

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  17. What is the range of the function f(x)=(|x-1|)/((x-1))?

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  18. If A=[[cos alpha,-sin alpha],[sin alpha,cos alpha]], then for what val...

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  19. What is the principal value of sin^(-1)(-(sqrt(3))/2)\ ?

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  20. Find the equation of the plane through the points (2, 1, 1) and (1, ...

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