Answer to Question #148578 in Analytic Geometry for Jyotiramay Rout
Denote by a, b and c the column vectors a = (1 2 3), b = (-2 1 -3), c = (-2 -1 1) Calculate 2a - 5b, 2a- 5b +c, a'.b,
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2020-12-04T12:52:08-0500
a=⎝⎛123⎠⎞,b=⎝⎛−21−3⎠⎞,c=⎝⎛−2−11⎠⎞
2a−5b=2⎝⎛123⎠⎞−5⎝⎛−21−3⎠⎞=⎝⎛2(1)−5(−2)2(2)−5(1)2(3)−5(−3)⎠⎞
=⎝⎛12−121⎠⎞
2a−5b+c=2⎝⎛123⎠⎞−5⎝⎛−21−3⎠⎞+⎝⎛−2−11⎠⎞
=⎝⎛12−121⎠⎞+⎝⎛−2−11⎠⎞=⎝⎛12−2−1−121+1⎠⎞=⎝⎛10−222⎠⎞
aT⋅b=(123)⋅⎝⎛−21−3⎠⎞
=1(−2)+2(1)+3(−3)=−9
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