 Good morning friends, I am Poojwa and today we will discuss the following question. Find mod of vector x if for a unit vector, vector a we are given that the dot product of vector x minus vector a and vector x plus vector a is equal to 12. Let us begin with the solution now. Now we are given that the dot product of vector x minus vector a and vector x plus vector a is equal to 12. This implies now we can write left and side as mod of vector x square plus vector x dot vector a minus vector a dot vector x minus mod of vector a square and this is equal to 12. This implies mod of vector x square plus vector x dot vector a minus vector x dot vector a because we have vector a dot vector x is equal to vector x dot vector a minus mod of vector a square is equal to 12. This implies mod of vector x square now we cancel out vector x dot vector a and minus vector x dot vector a minus mod of vector a square is equal to 12. This implies mod of vector x square minus 1 is equal to 12 since we are given that vector a is a unit vector therefore we have mod of vector a is equal to 1. This further implies mod of vector x square is equal to 12 plus 1 and we have this implies mod of vector x square is equal to 13 because 12 plus 1 is equal to 13 and this further implies mod of vector x is equal to root 13. So we have got mod of vector x as root 13. This is our answer hope you have understood the solution bye and take care.