 Good morning friends and poor one today. We will work out the following question find the projection of vector b plus vector c on vector a where vector a is equal to 2i cap minus 2j cap plus k cap vector b is equal to i cap plus 2j cap minus 2k cap and Vector c is equal to 2i cap minus j cap plus 4k cap Let us begin with the solution now Now we are given Vector a is equal to 2i cap minus 2j cap plus k cap Vector b is equal to i cap plus 2j cap minus 2k cap and Vector c is equal to 2i cap minus j cap plus 4k cap And we have to find the projection of vector b plus vector c on vector a Now the projection of a vector a on other vector b is given by vector a Dot vector b upon mod of vector b Now here the projection of vector b plus vector c on vector a is given by Applying this formula we get vector b plus vector c Dot vector a upon mod of vector a now Vector b plus vector c is equal to vector b is equal to i cap plus 2j cap minus 2k cap Plus vector c is equal to 2i cap minus j cap Plus 4k cap This is equal to i cap plus 2i cap is equal to 3i cap 2j cap minus j cap gives plus j cap and minus 2k cap plus 4k cap gives plus 2k cap Now putting all the values in one we get the projection of vector b plus vector c on vector a is equal to vector b plus vector c which is equal to 3i cap Plus j cap plus 2k cap Dot vector a which is equal to 2i cap minus 2j cap plus k cap Upon mod of vector a that is mod of 2i cap minus 2j cap plus k cap This is equal to 3 into 2 is 6 1 into minus 2 is minus 2 2 into 1 is 2 so we get 6 minus 2 plus 2 in numerator upon Now mod of 2i cap minus 2j cap plus k cap is equal to under root of 2 square plus minus 2 whole square Plus 1 square This is further equal to 6 upon under root of now 2 square is equal to 4 plus Minus 2 whole square is equal to 4 plus 1 square is equal to 1 This is equal to 6 upon under root 9 which is equal to 6 upon 3 and This is further equal to 2 So we have got our answer as 2 hope you have understood the solution. Bye and take care