 Hi friends and poor va and today we will discuss the following question find the unit vector in the direction of vector pq where p and q are the points 1, 2, 3 and 4, 5, 6 respectively. Let us now begin with the solution. Now let O be the origin then we have vector O is equal to 0 i cap plus 0 j cap plus 0 k cap. So we get then vector O p is equal to i cap plus 2 j cap plus 3 k cap because we have vector O p is equal to position vector of p minus position vector of O and we get that is equal to i cap plus 2 j cap plus 3 k cap and vector O q is equal to 4 i cap plus 5 j cap plus 6 k cap because vector O q is equal to position vector of q minus position vector of O and that is equal to 4 i cap plus 5 j cap plus 6 k cap. So we have vector pq is equal to vector O q minus vector O p and we have this is equal to now vector O q is equal to 4 i cap plus 5 j cap plus 6 k cap minus vector O p is equal to i cap plus 2 j cap plus 3 k cap. This is equal to now first we write the coefficients of i cap together so we have 4 minus 1 i cap plus we write the coefficients of j cap together so we get 5 minus 2 j cap plus we write the coefficients of k cap together so we get 6 minus 3 k cap and this is equal to 3 i cap plus 3 j cap plus 3 k cap so we have got vector pq is equal to 3 i cap plus 3 j cap plus 3 k cap. Now we have to find the unit vector in the direction of vector pq so for that first we will find mod of vector pq so mod of vector pq is equal to mod of 3 i cap plus 3 j cap plus 3 k cap and this is equal to under root of 3 square plus 3 square plus 3 square which is equal to under root of 9 plus 9 plus 9 and this is equal to under root of 27 so we get mod of vector pq is equal to 3 root 3. Now let the unit vector in the direction of vector pq is given by n cap therefore we have n cap is equal to vector pq upon mod of vector pq and this is equal to now vector pq is equal to 3 i cap plus 3 j cap plus 3 k cap upon mod of vector pq is equal to 3 root 3 and we have this is equal to 1 upon root 3 i cap plus 1 upon root 3 j cap plus 1 upon root 3 k cap so we have n cap is equal to 1 upon root 3 i cap plus 1 upon root 3 j cap plus 1 upon root 3 k cap hence the unit vector in the direction of vector pq is given by 1 upon root 3 i cap plus 1 upon root 3 j cap plus 1 upon root 3 k cap this is our answer hope you have understood the solution bye and take care