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Determine whether the pair of straight l...

Determine whether the pair of straight lines
`vecr=(2hati+6hatj+3hatk)+t(2hati+3hatj+4hatk),vecr=(2hatj-3hatk)+s(hati+2hatj+3hatk)` are parallel. Find the shortest distance between them.

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Determine whether the pair of straight lines vecr=(2hati+6hatj+3hatk)+t(2hati+3hatj+4hatk),vecr=(2hati-3hatk)+s(hati+2hatj+3hatk) are parallel.

Determine whether the lines vecr=(hati-hatj)+t(hati-hatj+3hatk) and vecr=(2hati+hatj-hatk)+s(hati+2hatj-hatk) are parallel. Find the shortest distance between them.

Show that the lines vecr=(3hati+5hatj+7hatk)+t(hati-2hatj+hatk) vecr=(hati+hatj+hatk)+s(7hati+6hatj+7hatk) are skew lines and find the shortest distance between them.

Show that the lines vecr=(6hati+hatj+2hatk)+s(hati+2hatj-3hatk) and vecr=(3hati+2hatj-2hatk)+t(2hati+4hatj-5hatk) are skew lines and hence find the shortest distance between them.

Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-hatj+hatk) and vecr=(2hati+hatj-hatk)+s(2hati-hatj+hatk) .

Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hatj)+s(hati+hatj-hatk) are skew lines and find the distance between them .

Find the angle between the following lines. vecr=(4hati-hatj)+t(hati+2hatj-2hatk) vecr =(hati-2hatj+4hatk)+s(-hati-2hatj+2hatk)

Show that the lines vec r = hati + hatj + t(hati - hatj +3hatk) and vecr = 2hati + hatj -hatk + s(hati + 2hatj -hatk) intersect . Find the point of intersection.

SURA PUBLICATION-MODAL QUESTION PAPER-PART - III
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  2. In a competitive examination, one mark is awarded for every correct an...

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  3. State triangle inequality.

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  4. Find the condition that the roots of ax^(3)+bx^(2)+cx+d=0 are in geome...

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  5. Find the domain of sin^(-1)(2-3x^(2)).

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  6. Find the equation of the parabola with vertex (-1, -2), axis parallel ...

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  7. if the normal at the point t(1) on the parabola y^(2) = 4ax meets ...

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  8. If hat(a),hat(b),hat(c) are three unit vectors such that hat(b)andhat(...

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  9. Determine whether the pair of straight lines vecr=(2hati+6hatj+3hatk...

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  10. Prove that tan(pi/4+1/2cos^(-1)(a/b))+tan(pi/4-1/2cos^(-1)(a/b))=(2b)/...

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  11. If F (alpha)= [{:(cosalpha,0, sinalpha),(0,1,0),(-sinalpha,0,cosalpha)...

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  12. Find the values of the real numbers x and y, if the complex numbers ...

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  13. Find a polynomial equation of minimum degree with rational coefficient...

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

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  15. The parabolic communication antenna has a focus at 2 m distance from t...

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  16. Prove that [vecaxxvecb,vecbxxvecc,veccxxveca]=[veca,vecb,vecc]^(2)

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  17. Evaluate lim(xto0^(+))(1/x-1/(e^(x)-1)).

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  18. Evaluate int(-1)^(1)log((3-x)/(3+x))dx.

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  19. From the differential equations by eliminating arbitrary constants giv...

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  20. Draw the Geometrical diagram for the sum of two complex numbers, z(1)a...

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