 Hi friends, I am Poojwa and today I will solve the following question show that the points a 1, 2, 7 b 2, 6, 3 and c 3, 10, minus 1 are collinear Let us begin with the solution now Now we are given that a is 1, 2, 7 b is 2, 6, 3 and c is 3, 10, minus 1 and We have to show that points a b and c are collinear So first we find vector a b and we have this is equal to 2i cap plus 6j cap plus 3k cap minus 1i cap plus 2j cap plus 7k cap and we get this is equal to 2 minus 1i cap plus 6 minus 2j cap plus 3 minus 7k cap This is equal to 1i cap plus 4j cap minus 4k cap So we have got vector a b is equal to 1i cap plus 4j cap minus 4k cap Now mod of vector a b is equal to under root of 1 square plus 4 square plus minus 4 square and this is equal to under root of 1 plus 16 plus 16 and this is equal to root 33 so mod of vector a b is equal to root 33 Now vector bc is equal to 3i cap plus 10j cap minus k cap minus 2i cap plus 6j cap plus 3k cap This is equal to 3 minus 2i cap plus 10 minus 6j cap plus minus 1 minus 3k cap and this implies vector bc is equal to 1i cap plus 4j cap minus 4k cap Now mod of vector bc is equal to under root of 1 square plus 4 square plus minus 4 square and this is equal to under root of 1 plus 16 plus 16 and This is equal to root 33 so mod of vector bc is equal to under root 33 Now finally vector ac is equal to 3i cap plus 10j cap minus k cap minus i cap plus 2j cap plus 7k cap and this is equal to 3 minus 1i cap plus 10 minus 2j cap plus minus 1 minus 7k cap which is equal to 2i cap plus 8j cap minus 8k cap So we have got vector ac is equal to 2i cap plus 8j cap minus 8k cap So we get mod of vector ac is equal to under root of 2 square plus 8 square plus minus 8 square and This is equal to under root of 4 plus 64 plus 64 Which is equal to under root 132 and we can write this as This implies mod of vector ac is equal to 2 root 33 Therefore we can clearly see that mod of vector ab plus mod of vector bc is equal to under root 33 plus under root 33 Which is equal to 2 under root 33 and this is equal to mod of vector ac and Therefore we get points a b and c are Collinear this is our answer. Hope you have understood the solution. Bye and take care