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Find the Cartesian form of the equation of the plane `vec(r)=(s-2t)hat(i)+(3-t)hat(j)(2s+t)hat(k)`

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Find the equation the plane which contain the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec r(5 hat i+3 hat j-6 hat k)+8=0 .

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FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
  1. Find the vector and cartesian equations of the plane containing the li...

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  2. Derive the equation of the plane in the intercept form.

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  3. Find the Cartesian form of the equation of the plane vec(r)=(s-2t)hat(...

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  4. Show that the straigh lines vecr=(veci+vecj-veck)+lambda(3veci-vecj)...

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  5. If the straight lines (x-1)/(2)=(y+1)/(lamda)=(z)/(2)and(x+1)/(5)=(y+1...

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  6. If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/...

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  7. Show that the lines (x+3)/(-3)=(y-1)/(1)=(z-5)/(5) and (x+1)/(-1)...

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  8. Find the point of intersection of the line passing through the two poi...

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  9. Find the coordinates of the point where the line vecr=(hati+2hatj-5ha...

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  10. Find the point of intersection of the line vecr=(vecj-veck)+s(2veci-...

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  11. Find the meeting point of the line vecr=(2veci+vecj-3veck)+t(2veci-v...

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  12. Show that the following planes are at right angles: vecr.(2veci+vec...

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  13. The planes vecr.(2vec+lambdavecj-3veck)=10 and vecr.(lambdavec+3ve...

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  14. Find the angle between the line (x-2)/(3)=(y-1)/(-1)=(z-3)/(2)" and th...

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  15. Find the angle between the line vecr=veci+vecj+3veck+lambda(2veci+ve...

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  16. If veca=2veci+vecj-veck , vecb=veci+2vecj+veck and vecc=veci-v...

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  17. If veca=hati-hatk,vecb=xhati+hatj+(1-x)hatk,vecc=yhati+xhatj+(1+x-y)h...

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  18. If veca , vecb , vecc are three non-coplanar vector and vecp...

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  19. The value of hati.(hatjxxhatk)+hatj.(hatkxxhati)+hatk.(hatjxxhati) ...

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  20. Let a,b,c be distinct non-negative numbers. If the vectors ahati+ahatj...

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