Let O A, O B, O C be the co-terminal edges of a rectangular parallelopiped of volume V and let P be the vertex opposite to O . Then, [ A P B P C P ] is equal to

Step-by-step solution

Here, O A, O B, O C are the co-terminal edges of a rectangular parallelopiped of volume V . Also, we know that the volume of rectangular parallelopiped =[ a b c ] ie, V=[ OA OB OC ] (i) Let OA = a , OB = b , OC = c then from figure AP = a + b , BP = b + c , CP = c + a (By vector addition) Now, we find [ AP BP CP ]=[( a + b )( b + c )( c + a )]=( a + b ) [( b + c ) ( c + a )]=( a + b ) [ b c + b a + c c + c a ][ c c =0] array l a b = c b c = a c a = b array .=( a + b ) [ a - a b +0+ b ]=( a + b ) [ a - c + b ]=( a +