Question #213696

Determine whether ~u and ~v are orthogonal vectors, make an acute or obtuse angle: (1.1) ~u =< 1, 3, −2 >, ~v =< −5, 3, 2 >. (2) (1.2) ~u =< 1, −2, 4 >, ~v =< 5, 3, 7 >.


1
Expert's answer
2021-07-26T14:16:40-0400

Let us determine whether ~u and ~v are orthogonal vectors, make an acute or obtuse angle using dot product of vectors.


(1.1) Since the dot product

~uu\cdot~v=<1,3,2><5,3,2>=1(5)+33+(2)2=5+94=0,v =< 1, 3, −2 >\cdot< −5, 3, 2 >=1(-5)+3\cdot 3+(-2)\cdot 2=-5+9-4=0, we conclude that two vectors are orthogonal.


(1.2) Since the dot product

~uu\cdot~u =<1,2,4><5,3,7>=15+(2)3+48=56+32=31>0,< 1, −2, 4 >\cdot< 5, 3, 7 >=1\cdot 5+(-2)\cdot 3+4\cdot 8=5-6+32=31>0, we conclude that two vectors make an acute angle.


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