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Show that the straigh lines vecr=(veci...

Show that the straigh lines ` vecr=(veci+vecj-veck)+lambda(3veci-vecj) `
` vecr=(4veci-veck)+mu(2veci+3veck) ` are coplanar . Find the vector equation of the which they lie.

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Show that the lines vecr=(4veci+5vecj+6veck)+t(2veci+3vecj+4veck) and vecr=(2veci+3vecj+4veck)+s(3veci+4vecj+5veck) are coplanar. Find the equation of the plane in which they lie.

Find the angle between the line vecr=veci+vecj+3veck+lambda(2veci+vecj-veck) and the plane vecr.(veci+vecj)=1

find the shortest distance between the skew lines. vecr=(veci-vecj)+lambda(2veci+vecj+veck) and vecr=(veci+vecj-veck)+mu(2veci-vecj-veck)

Show that the following planes are at right angles: vecr.(2veci+vecj+veck)=15 and vecr.(veci+vecj-3veck)=3 .

Show that the points whose position vectors are 4veci +5vecj+veck , -vecj-veck , and 3veci+9vecj +4veck and -4veci+4vecj+4veck are co planar.

Find the angle between the vectors 3veci-4vecj+veck and veci-3vecj+4veck .

find the shortest distance between the skew lines. vecr=(2veci-vecj-veck)+t(veci-2vecj+3veck) and vecr=(veci-2vecj-veck)+s(2veci-2vecj-3veck)

Find (veci+vecj).{(vecj+veck) X (veck+veci)} :

Find the angle between the following lines vecr=3veci+2vecj-veck+t(veci+2vecj+2veck) and vecr=5vecj+2veck+s(3veci+2vecj+6veck)

Given that veca=veci-vecj-veck , vecb=2veci-vecj+veck , find (2veca+3vecb).(veca-2vecb) .

FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
  1. Derive the equation of the plane in the intercept form.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. The value of hati.(hatjxxhatk)+(hatixxhatk).hatj …….

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