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Find the shortest distance between the lines ` vec r=(1-lambda) hat i+(lambda-2) hat j+(3-2lambda) hat k` and `vec r=(mu+1) hat i+(2mu+1) hat kdot`

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

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot(( hat i+5 hat j+ hat k))=5.

Find the shortest distance between the two lines whose vector equations are : vec(r)=(1-t)hat(i)+(t-2)hat(j)+(3-t)hat(k), vec(r)=(s+1)hat(i)+(2s-1)hat(j)-(2s+1)hat(k)

Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+lambda( hat i- hat j+ hat k) and the plane vec r . dot(3 hat i- hat j+ hat k)=4.

Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k) a n d vec r=(5 hat j-2 hat k)+mu(3 hat i+2 hat j+6 hat k)dot

The Cartesian equation of the plane vec r=(1+lambda-mu) hat i+(2-lambda) hat j+(3-2lambda+2mu) hat k is a. 2x+y=5 b. 2x-y=5 c. 2x+z=5 d. 2x-z=5

Find the angel between the following pair of lines: vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)a n d vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k) x/2=y/2=z/1a n d(x-5)/4=(y-2)/1=(z-3)/8

Find the distance between the lines l_(1) and l_(2) given by vec(r)=(hat(i)+2hat(j)-4hat(k))+lamda(2hat(i)+3hat(j)+6hat(k)) and vec(r)=(3hat(i)+3hat(j)-5hat(k))+mu(2hat(i)+3hat(j)+6hat(k))

The shortest distance (in units) between the lines vec(r)=(hat(i)+2hat(j)+4hat(k))+t(5hat(j))" and "vec(r)=(hat(i)+2hat(j)+5hat(k))+s(hat(j)) is

Find the shortest distance between the two lines whose vector equations are : vec(r)=(hat(i)+hat(j))+t(2hat(i)-hat(j)+hat(k)), vec(r)=(2hat(i)+hat(j)-hat(k))+s(3hat(i)-5hat(k)+2hat(k))

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