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Find the distance between the lines over...

Find the distance between the lines `overset(to)(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda ( 2 hat(i) + 3 hat(j) + 6 hat(j) ) & overset(to)(r ) = 3 hat(i) + 3 hat(j) - 5 hat(k) + mu ( -2 hat(i) + 3 hat(j) + 8 hat(k) )`

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The correct Answer is:
`d= ( sqrt( 293))/( 7) `
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Find the shortest distance between two lines whose vector equations are vec(r) = (hat(i) + 2 hat(j) + 3 hat(k))+lambda(hat(i)- 3hat(j) + 2 hat(k)) and vec(r) = (4 hat(i) + 5 hat(j) + 6 hat(k))+ mu (2 hat(i)+3 hat(j) + hat(k)) .

Find angle between the vectors overset(to)(a) = hat(i) + hat(j) - hat(k) and overset(to)(b) = hat(i) + hat(j) + hat(k)

Find the shortest distance between the lines whose vector equations are vec(r) = (hat(i) + hat(j)) + lambda(2 hat(i) - hat(j) + hat(k)) and vec(r) = (2 hat(i) + hat(j) - hat(k)) + mu (3 hat(i) - 5 hat(j)+2 hat(k)) .

Find the vector and cartesian equations of a plane containing the two lines vec(r) = (2 hat(i) + hat(j) - 3 hat(k)) + lambda(hat(i) + 2 hat(j) + 5 hat(k)) and vec(r) = (3hat(i) + 3 hat(j) + 2 hat(k)) + lambda (3 hat(i) - 2 hat(j) + 5 hat(k)) . Also show that the line vec(r) = (2 hat(i) + 5 hat(j) + 2 hat(k)) + p (3 hat(i) - 2 hat(j) + 5 hat(k)) lies in the plane.

Find the sine of the angle between the vectors hat(i) + 2 hat(j) + 2 hat(k) and 3 hat(i) + 2 hat(j) + 6 hat(k)

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

Find lambda if the vectors overset(to)(a) = hat(i) +3 hat(j) + hat(k) , overset(to)(b) = 2hat(i) - hat(j) - hat(k) and overset(to) (c ) = lambda hat(i) + 7 hat(j) + 3 hat(k) are coplanar

Find the equation of the plane passing through the point P(1,1,1) and containing the line vec(r) = (-3 hat(i) + hat(j) + 5 hat(k)) + lambda (3 hat(i) - hat(j) - 5 hat(k)) . Also, show that the plane contains the line vec(r) = (- hat(i) + 2 hat(j) + 5hat(k)) + mu (hat(i) - 2 hat(j) - 5 hat(k)) .

SUNSTAR PUBLICATION-ANNUAL EXAM QUESTION PAPER MARCH - 2016-PART - C (Answer any ten questions)
  1. Find two numbers whose product is 100 and whose sum is minimum.

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  2. Find the area lying between the curve y^(2) = 4x and the line y=2x

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  3. For any three vectors overset(to)(a) , overset(to)(b) and overset(to) ...

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  4. Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j...

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  5. Find the sine of the angle between the vectors hat(i) + 2 hat(j) + 2 h...

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  6. Find the equation of the curve passing through the point (1,1), given ...

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  7. Show that tan^(-1)""(1)/(2) + tan^(-1)""(2)/( 11) + tan^(-1)""(4)/(3) ...

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  8. Using elementary transformations, find the inverse of the matrices ...

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  9. Show that the relation R in the set A={x in Z :0lexle12} is given by R...

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  10. Verify Mean Value Theorem if f(x)= x^(3) - 5x^(2) - 3x in the interval...

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  11. If x=a cos ^(3) theta and y = a sin^(3) theta then (dy)/( dx) =

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  12. Box-I contains 2 gold coins, while another Box-II contains 1 gold and...

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  13. Find int(xdx)/((x+1)(x+2))

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  14. Integrate (2x)/( ( x^(2) + 1) ( x^(2) + 2) ) with respect to x.

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  15. Find two numbers whose product is 100 and whose sum is minimum.

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  16. Find the area lying between the curve y^(2) = 4x and the line y=2x

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  17. For any three vectors overset(to)(a) , overset(to)(b) and overset(to) ...

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  18. Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j...

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  19. Find the sine of the angle between the vectors hat(i) + 2 hat(j) + 2 h...

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  20. Find the equation of the curve passing through the point (1,1), given ...

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