If the direction cosines of a line are ( a 83 , 5 83 , c 83 ) and c-a=4 , then c a=

Step-by-step solution

Direction cosine of a i +b j +c k can be a a^2+b^2+c^2 , b a^2+b^2+c^2 , c a^2+b^2+c^2 According to question, a^2+b^2+c^2 = 83 , b=5 a^2+(5)^2+c^2=83 a^2+c^2=83-25 a^2+c^2=58 ...(i) and c-a=4 [given] (c-a)^2+2 a c=a^2+c^2 (4)^2+2 a c=58 [from Eq. (i), .c^2+a^2=58 ] 2 a c=58-16a c= 42 2 =21