Answer to Question #278620 in Analytic Geometry for Nofiu pelumi

Question #278620

Find the vector that has (a) the same direction as A and twice the magnitude of A, (b) the opposite direction of a and one-third the magnitude of a, and (c) the same direction as A and magnitude 2.


(i)A=14i-15j+6k


1
Expert's answer
2021-12-14T14:07:47-0500

(a)


2A=28i30j+12k2\vec A=28\vec i-30\vec j+12\vec k

(b)


13A=143i+5j2k-\dfrac{1}{3}\vec A=-\dfrac{14}{3}\vec i+5\vec j-2\vec k

(c)


A=(14)2+(15)2+(6)2=457|\vec A|=\sqrt{(14)^2+(-15)^2+(6)^2}=\sqrt{457}

2457A=28457i30457j+12457k\dfrac{2}{\sqrt{457}}\vec A=\dfrac{28}{\sqrt{457}}\vec i-\dfrac{30}{\sqrt{457}}\vec j+\dfrac{12}{\sqrt{457}}\vec k


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