Vector A has a magnitude of 12.0 units and points due west. Vector B points due north. (a) Magnitude of B if A+B is 14.4 units? (b) Direction of A+B relative to due west? (c) Magnitude of B if A-B has 14.4 units (d) Direction of A-B rel. to due west?

1 Answer
Jan 17, 2018

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Here,angle between the given two vectors is #90#,so if #A+B =14.4# we can say, #(A+B)^2 = A^2 +B^2 + 2AB cos 90# ,so# B = 7.95# units.

if direction of #A+B# makes an angle of #theta# w.r.t west i.e vector# A# we can say #tan theta# = #(B/A)# or #theta# = #33.52#

similarly, if# A-B# is #14.4#, #B# will also be #7.95# (refer to equation of vector sum),and it will also make #33.52# degrees w.r.t west