सिद्ध कीजिए की `x=py +q,z= ry + s ` तथा ` x=p'y +q' ,z=r'y +s'` रेखाएं परस्पर लम्ब है,यदि `pp' +rr'+1=0`

Prove that the lines x = py + q, z = ry + s and x = p'y + q', z = r'y + s' are perpendicular if pp' + rr' + 1 = 0.

Prove that the lines x=py+q, z=ry+s and x=p'y+q'z=r'y+s' are at right angles if pp'+rr'+1=0.

Find the condition that the lines x=py +q, z=ry +s and x=p'y +q', z= r'y+s' may be perpendicular to each other.

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

If [[ p , q-y , r-z],[ p-x , q , r-z ],[ p-x , q-y , r ]]=0 , then (p)/(x)+(q)/(y)+(r)/(z)=

Show that: |b+c c+a a+b q+r r+p p+q y+z z+x x+y|=2|a b c p q r x y z|