उस समतल का समीकरण ज्ञात कीजिए, जो तीन बिंदुओं `A(-2 hati + 6 hati j - 6 hatk), B (-3 hati + 10 hatj - 3 hatk )` तथा `C (-5hati - 6 hatk )` से गुजरता है |

यदि A (-hati + 3hatj + 2hatk) , B (-4hati + 2hatj - 2hatk) तथा C(5hati + (lambda +1)hatj + mu hatk) संरेखीय है तब :

Show that the points A(-2 hati+3 hatj+5 hatk) , B(hati+2 hatj+3 hatk) and C(7 hati-hatk) are collinear.

Show that the points : A(-2hati+3hatj+5hatk), B(hati+2hatj+3hatk) and C(7hati-hatk) are collinear.

If a = 2 hati + j - 3 hatk , b = hati - 2 hatj + 3hatk , c = - hati + hatj - 4hatk and d = hati + hatj + 2hatk , then (a xx b) xx ( c xx d) =

The shortest distance between the lines r = ( - hati - hatj - hatk ) + lamda ( 7 hati - 6 hatj + hatk ) and r = ( 3 hati + 5 hatj + 7 hatk ) + mu ( hati - 2 hatj + hatk )

If vecA= 5hati+6hatj+3hatk and vecB=6hati-2hatj-6hatk , then

Find the angle between the following pairs of lines : (i) vec(r) = 2 hati - 5 hatj + hatk + lambda (3 hati + 2 hatj + 6 hatk ) and vec(r) = 7 hati - 6 hatk + mu (hati + 2 hatj + 2 hatk) (ii) vec(r) = 3 hati + hatj - 2 hatk + lambda (hati - hatj - 2 hatk ) and vec(r) = 2 hati - hatj - 56 hatk + mu (3 hati - 5 hatj - 4 hatk) .