 Good morning friends, I am Purva and today we will discuss the following question. Find the sum of the vectors vector A is equal to i cap minus 2 j cap plus k cap vector B is equal to minus 2 i cap plus 4 j cap plus 5 k cap and vector C is equal to i cap minus 6 j cap minus 7 k cap. Let us now begin with this solution. Now we are given vector A is equal to i cap minus 2 j cap plus k cap vector B is equal to minus 2 i cap plus 4 j cap plus 5 k cap and vector C is equal to i cap minus 6 j cap minus 7 k cap. And we have to find the sum of these three vectors that is we have to find vector A plus vector B plus vector C is equal to what? So we have vector A is equal to i cap minus 2 j cap plus k cap plus vector B is equal to minus 2 i cap plus 4 j cap plus 5 k cap plus vector C is equal to i cap minus 6 j cap minus 7 k cap. This is equal to now first we write the coefficients of i cap together. So here we have the coefficient of i cap as 1 so 1 here the coefficient of i cap is minus 2 so minus 2 and here the coefficient of i cap is 1 so plus 1 i cap plus now we will write the coefficients of j cap together so minus 2 here the coefficient of j cap is 4 so plus 4 and here the coefficient of j cap is minus 6 so minus 6 j cap plus now we will write the coefficients of k cap together so here the coefficient of k cap is 1 so 1 plus here the coefficient of k cap is 5 so 5 and here the coefficient of k cap is minus 7 so minus 7 k cap and this is equal to now 1 plus 1 is equal to 2 and 2 minus 2 gives 0 so we have 0 i cap minus 2 minus 6 gives minus 8 plus 4 gives minus 4 so minus 4 j cap 1 plus 5 is equal to 6 minus 7 gives minus 1 so minus 1 k cap and we can write this as this is equal to minus 4 j cap minus k cap hence we have got the sum of the vectors a b and c is equal to minus 4 j cap minus k cap this is our answer hope you have understood the solution bye and take care