If #A= <-3, -1 ># and #B= <-2, 5 >#, what is #||A+B|| -||A|| -||B||#? Trigonometry Trigonometric Identities and Equations Products, Sums, Linear Combinations, and Applications 1 Answer ali ergin Mar 14, 2016 #||A+B||-||A-B||=sqrt41-sqrt37# Explanation: #A=(A_x,A_y,A_z)" "B=(B_x,B_y,B_z)# #A+B=(A_x+B_x,A_y+B_y,A_z+B_z)# #A-B=(A_x-B_x,A_y-B_y,A_z-B_z)# #A+B=(-5,4)# #A-B=(-1,-6)# #||A+B||=sqrt((-5)^2+4^2)=sqrt(25+16)=sqrt41# #||A-B||=sqrt((-1)^2+(-6^2)=sqrt(1+36)=sqrt(37)# #||A+B||-||A-B||=sqrt41-sqrt37# Answer link Related questions How do you use linear combinations to solve trigonometric equations? How do you derive the multiple angles formula? How do you apply trigonometric equations to solve real life problems? How do you use the transformation formulas to go from product to sum and sum to product? What is the sum to product formulas? How do you change #2 \sin 7x \cos 4x# into a sum? How do you solve #sin 4x + sin 2x = 0# using the product and sum formulas? How do you use the sum and double angle identities to find sin3x? How do you simplify #sin^2theta-cos^2theta+tan^2theta# to non-exponential trigonometric functions? How do you simplify #sin^2theta# to non-exponential trigonometric functions? See all questions in Products, Sums, Linear Combinations, and Applications Impact of this question 1173 views around the world You can reuse this answer Creative Commons License