Given vector A= 3 i cap + j cap + 4k cap and vector B = i cap + 3 j cap - 5 k cap. Find the unit vector in the direction of (vector A+ vector B) and (vector A - vector B)

Answer 1

A+B=4i+4j-k. Find the magnitude of A+B: mag(A+B)=sqrt(16+16+1)=sqrt(33). So the unit vector of A+B is (1/sqrt(33))*(4i+4j-k). A-B=2i-2j+9k. mag(A-B)=sqrt(4+4+81)=sqrt(89).The unit vector of A-B is (1/sqrt(89))*(2i-2j+9k)