The lines `vecr = (hati + hatj + hatk ) alpha + 3hatk and vecr = (hati -2hatj+hatk)beta + 3hatk`

If d is the shortest distance between the lines vecr =(3hati +5hatj + 7hatk)+lambda (hati +2hatj +hatk) and vecr = (-hati -hatj-hatk)+mu(7hati-6hatj+hatk) then 125d^(2) is equal to ____________.

Find the shortest distance between the lines vecr = hati+hatj+lambda(2hati-hatj+hatk) and vecr = (2 hati+hatj-hatk) + mu (3hati-5hatj + 2hatk)

The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and vecr=(hati+2hatj+3hatk)+mu(3hati+phatj+phatk) are perpendicular it p=

Find the shortest distance between the lines vecr = 2hati - hatj + hatk + lambda(3hati - 2hatj + 5hatk), vecr = 3hati + 2hatj - 4hatk + mu(4hati - hatj + 3hatk)

The line vecr=alpha(hati+hatj+hatk)+3hatk and vecr=beta(hati-2hatj+hatk)+3hatk (A) intersect at rilghat angles (B) are skew (C) are parallel (D) none of these

Find shortest distance between the line vecr = (5hati + 7hatj + 3hatk )+lambda (5hati-6hatj+2hatk)and vecr = (9hati+13hatj+15hatk)+s (-3hati+hatj-hatk)

If vecr = hati + hatj + lamda( 2 hati + hatj + 4 hatk ) and vecr (hati + 2 hatj - hatk)=3 are the equations of a line and a plane respectively then which of the following is true ?

Find the shortest distance between the lines vecr = hati+ hatj+hatk+lambda(3hati-hatj) and vecr=4hati-hatk+mu(2hati+3hatk)

The line whose vector equation are vecr =2 hati - 3 hatj + 7 hatk + lamda (2 hati + p hatj + 5 hatk) and vecr = hati - 2 hatj + 3 hatk+ mu (3 hati - p hatj + p hatk) are perpendicular for all values of gamma and mu if p equals :

The acute angle between the lines vecr=(4hati-hatj)+lamda(2hati+hatj-3hatk) and vecr=(hati-hatj+2hatk)+t(hati-3hatj+2hatk) is (A) (3pi)/2 (B) pi/3 (C) (2pi)/3 (D) pi/6