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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 the projection of vec(a) = 2 hat(i) - hat(j) + hat(k) on vec(b) = hat(i) - 2 hat(j) + hat(k) .

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

Find a unit vector perpendicular to each one of the vectors vec(a) = 4 hat(i) - hat (j) + 3hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) .

Find the scalar projection of vec(b) on vec(a) , when : vec(a)=2hat(i)+2hat(j)-hat(k) and vec(b)=2hat(i)-hat(j)-4hat(k)

What is the projection of vec(a)=(2hat(i)-hat(j)+hat(k)) on vec(b)=(hat(i)-2hat(j)+hat(k))?

Find the unit vectors perpendicular to the plane of the vectors vec(a) = 2 hat(i) - 6 hat(j)- 3 hat(k) and vec(b)= 4 hat(i) + 3 hat(j) - hat(k).

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 :

Find a unit vector perpendicular to each one of the vectors vec(a)= ( 4 hat(i) - hat(j)+ 3 hat(k)) and vec(b)=(2hat(i) + 2 hat(j)- hat(k)).

If vec(a) = 2hat(i) + hat(j) - hat(k) and vec(b) = hat(i) - hat(k) , then projection of vec(a) on vec(b) will be :

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

XII BOARDS PREVIOUS YEAR-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)

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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: (y+3x^2)(dx)/(dy)=x

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  12. A speaks truth in 60% and Bin 80% of the cases. In what percentage of ...

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  13. If vec a and vec b are two vectors such that | vec a+ vec b|=| vec a...

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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...

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  16. If y=(s in^(-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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