Question

Consider the vector v = (14, 14, 4). Find u such that the following is true. he vector u has the same direction as v and one-half its length. u = (b) The vector u has the direction opposite that of v and one-fourth its length. U = (c) The vector u has the direction opposite that of v and twice its length. U =

Answer 1

So, o vector o has same direction ОО and one half uts clength. SOLO Here the given vector is v= (14, 14, 4 ) Therefore the required length of vector is. lluil = J14²+14²+42 = June and unit vector in same direction of vis (14,14,4) livil Jчо vnit vector in opposite direction of vij (1431414 Juca IV ) @ in same as Now, seariced lector u, whose direction N and one - hall uts length: = I livil. (5)

= I (14, 14, 4) sa 10=(772) Auswer alone (ule) In this case reaniced Vector u, whose sahne a opposite of u and one-fourth direction is of uts length ? u= I lv. C-1)(x ) U= 0 + (-14, -14,-4) u= (-2,-2 ,-1) is opposite (e) In these case required vector u, whose direction of vand twice of uts length ? = 2101.coli = 2 (-14, -14,-4) = (-28,-28,-8)