The lines `vecr = (i +j+k)alpha + 3k` and `vecr = (i-2j+k)beta + 3k`

The lines vec r=(i+j+k)alpha+3k and vec r=(i-2j+k)beta+3k

The lines vec r=(hat i+hat j+hat k)alpha+3hat k and vec r=(hat i-2hat j+hat k)beta+3hat k

the shortest distance between the skew lines vec r=3i+8j+3k+alpha(3i-j+k) and vec r=-3i-7j+6k+beta(-3i+2j+4k)

The lines vec r=i-j-k+s(i+2j-2k) and vec r=(i-2j+3k)+t(-i+j-2k)

The lines r = i + j - k + lambda (3i - j) and r = 4i - k + mu (2i + 3k) intersect at the point

Show that the lines vecr= (hat i+hat j+hat k)+t(hat i-hat j+hat k) and vecr= (3 hati-hatk)+s(4 hat j-16 hat k) intersect and find the position vector of their point of their point of intersection.

Show that the equation of the planes are perpendicular to each other. vecr.(2 hat i- hat j+3 hat k)=5 and vecr.(2 hat i- 2 hat j - 2 hat k)=5