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.Find out whether the following pairs of lines are parallel, non-parallel & intersecting, or non-parallel & non-intersecting `hati_1 =hat i +hat j + 2hat k + lambda (3hat i-2hat j+4hat k) and r_2 =hat i +hat j + 3hat k + mu (-6hat i +4hat j-8hat k) `

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parallel
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Find out whether the following pairs of lines are parallel, non parallel, & intersecting, or non-parallel & non-intersecting. vec(r_(1)) = hat(i) - hat(j) + 3hat(k) + lambda(hat(i) - hat(j)+hat(k)) vec(r_(2)) = hat(i) - hat(j) + 3hat(k) + lambda(hat(i) - hat(j) + hat(k)) vec(r_(2)) = 2hat(i) + 4hat(j) + 6hat(k) + mu (2hat(i) + hat(j) + 3hat(k))

Find out whether the following pairs of lines are parallel, non parallel, & intersecting, or non-parallel & non-intersecting. vec(r_(1)) = hat(i) - hat(j) + lambda(hat(i) + 3hat(j) + 4hat(k)) vec(r_(2)) = 2hat(i) + 3hat(j) + mu(4hat(i) - hat(j) + hat(k))

vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Shortest distance between the lines: vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+u(2hat i+4hat j-5hat k)

underset with a = 2hat i + hat j-3hat k, vec b = -hat i + hat j + 2hat k, vec c = 4hat i + 3hat k

If vec r=(hat i+2hat j+3hat k)+lambda(hat i-hat j+hat k) and vec r=(hat i+2hat j+3hat k)+mu(hat i+hat j-hat k) are bisector of two lines is

Find the shortest distance between the lines vec r=(hat i+2hat j+hat k)+lambda(hat i-hat j+hat k) and ,vec r,=2hat i-hat j-hat k+mu(2hat i+hat j+2hat k)

Find the shortest distance between the lines vec r=(hat i+2hat j+hat k)+lambda(hat i-hat j+hat k) and vec r=(2hat i-hat j-hat k)+mu(2hat i+hat j+2hat k)

Find the shortest distance between the lines vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Determine whether the following pair of lines intersect or not. (1) vec r= hat i-5 hat j+lambda(2 hat i+ hat k); vec r=2 hat i- hat j+mu( hat i+ hat j- hat k) (2) vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j); vec r=4 hat i- hat k+mu(2 hat i+3 hat k)

MOTION-VECTOR -EXERCISE - 3
  1. For any two vectors veca and vecb, prove that ((veca )/(|vec a |^2)-...

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  2. Given that vecx + 1/(vecp)^2 (vecp . vecx) vecp = vecq , show that vec...

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  3. .Find out whether the following pairs of lines are parallel, non-paral...

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  4. Find out whether the following pairs of lines are parallel, non parall...

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  5. Find out whether the following pairs of lines are parallel, non parall...

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  6. Let O A C B be a parallelogram with O at the origin andO C a diagonal....

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  7. Find the shortest distance between the lines : vec(r) = (4hat(i) - ha...

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  8. Let vec(A) = 2hat(i) + hat(k), vec(B) = hat(i) + hat(j) + hat(k) and ...

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  9. Find vector vec(v) which is coplanar with the vectors hat(i) + hat(j...

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  10. Find the point R in which the line AB cuts the plane CDE, where positi...

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  11. The position vectors of the angular points of a tetrahedron are A(3 ha...

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  12. Show that the four points with position vectors4 hat i+8 hat j+12 hat ...

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  13. Examine for coplanarity of the following sets of points 3vec(a) + 2...

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  14. The length of the edge of the regular tetrahedron DABC is 'a'. Point E...

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  15. The position vectors of the four angular points of a tetrahedron ar...

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  16. The position vectors of the four angular points of a tetrahedron ar...

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  17. The position vectors of the four angular points of a tetrahedron ar...

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  18. The position vectors of the four angular points of a tetrahedron ar...

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  19. ABCD is a tetrahedron with pv's of its angular point as A(-5, 22, 5); ...

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  20. Let vec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i) + hat(j) ...

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