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Find `lambda ` where projection of `vec (a) = lambda hat (i) + hat (j) + 4 hat (k) ` on `vec (b) = 2 hat (i) + 6 hat (i) + 3 hat (k) ` is 4 unit

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Find lambda, when the projection of vec a=lambda hat i+ hat j+4 hat k\ on\ vec b=2 hat i+6 hat j+3 hat k\ i s\ 4\ units.

Unit vectors perpendicular to the plane of vectors vec(a) = 2 hat(*i) - 6 hat(j) - 3 hat(k) and vec(b) = 4 hat(i) + 3 hat(j) - hat(k) are

Find the angle between vec(A) = hat(i) + 2hat(j) - hat(k) and vec(B) = - hat(i) + hat(j) - 2hat(k)

Determine lambda such that a vector vec(r) is at right angles to each of the vectors vec(a) = lambda hat(i) + hat(j) + 3hat(k), vec(b) = 2hat(i) + hat(j) - lambda hat(k), vec(c) = -2hat(i) + lambda hat(j) + 3hat(k) .

If the vectors vec (a) = 2 hat (i) - hat (j) + hat (k) , vec ( b) = hat (i) + 2 hat (j) - 3 hat (k) and vec(c ) = 3 hat (i) + lambda hat (j) + 5 hat (k) are coplanar , find the value of lambda

The value of lambda for which the two vectors vec(a) = 5hat(i) + lambda hat(j) + hat(k) and vec(b) = hat(i) - 2hat(j) + hat(k) are perpendicular to each other is :

If vec(a) = 2 hat(i) - hat(j) + hat(k) and vec(b) = hat(i) - 2 hat(j) + hat(k) then projection of vec(b)' on ' vec(a) is

Find the projection of the vector vec a=2 hat i+3 hat j+2 hat k on the vector vec b=2 hat i+2 hat j+ hat k .

Find the volume of the parallelopiped whose edges are represented by vec(a) = 2 hat(i) - 3 hat(j) + 4 hat(k) , vec(b) = hat(i) + 2 hat(j) - hat(k), vec(c) = 3 hat(i) - hat(j) + 2 hat(k)

Find the projection of vec(b)+ vec(c ) on vec(a) where vec(a)= 2 hat(i) -2hat(j) + hat(k), vec(b)= hat(i) + 2hat(j)- 2hat(k), vec(c ) = 2hat(i) - hat(j) + 4hat(k)

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Evaluate : int(1-x)sqrt(x)\ dxdot

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  2. Evaluate: int0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

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  3. Find lambda where projection of vec (a) = lambda hat (i) + hat (j) ...

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  4. If a line has direction ratios 2, –1, –2, then what are its directi...

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  5. Write the vector equation of the line given by (x-5)/3=(y+4)/7=(z-6...

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  6. Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4...

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  7. Using properties of determinants, solve the following for x: |[x-2, ...

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  8. If x=tan(1/alogy)\ , show that (1+x^2)(d^2\ y)/(dx^2)+(2x-a)(dy)/(dx)=...

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  9. Evaluate: int0^(pi/2)(x+sinx)/(1+cosx)dx

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  10. Solve the following differential equation: x\ dy-y\ dx=sqrt(x^2+y^2...

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  11. Solve the following differential equation: <math>  <mrow>   <mro...

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  12. A speaks truth in 60% of the cases, while B in 90% of the cases. In...

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  13. If vec a ,\ vec b ,\ are two vectors such that | vec a+ vec b|=| ve...

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  14. In answering a question on a multiple choice test, a student either...

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  15. An urn contains 4 white and 3 red balls. Let X be the number of red ba...

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  16. If y=(sin^(-1)\ x)/(sqrt(1-x^2)) , show that (1-x^2) (d^2\ y)/(dx^2)-...

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  17. Using properties of determinants, prove the following: |[1,1+p,1+p+q],...

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  18. On a multiple choice examination with three possible answers (out o...

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  19. If vec p is a unit vector and ( vec x-\ vec p).( vec x+\ vec p)...

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  20. Let f: NvecN be defined by f(n)={(n+1)/2,\ "if"\ n\ "i s\ o d d"n/2...

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