Question
Asked Sep 21, 2019
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For the vectors u (2, 1, 3) and v
(0, 3, 1), evaluate the following expressions.
Ju 4v
а. Зи + 2v
b. 4u v
c.
a. 3u 2v=
b. 4u v
lu 4v
+
C.
(Type an exact answer, using radicals as needed.)
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For the vectors u (2, 1, 3) and v (0, 3, 1), evaluate the following expressions. Ju 4v а. Зи + 2v b. 4u v c. a. 3u 2v= b. 4u v lu 4v + C. (Type an exact answer, using radicals as needed.)

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Expert Answer

Step 1

Given,  u = < 2, 1, 3 >   and   v = < 0, 3, 1 >

Step 2

(a)

3u 2v
3
2,1,3 > +2 < 0,3,1 >
=<3 x 2,3 x 1,3 x 3 > + < 2 x 0,2 x 3 ,2 x 1 >
=< 6,3,9 >< 0,6,2 >
=<6 0,3 6,9+ 2 >
=<6,9,11 >
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3u 2v 3 2,1,3 > +2 < 0,3,1 > =<3 x 2,3 x 1,3 x 3 > + < 2 x 0,2 x 3 ,2 x 1 > =< 6,3,9 >< 0,6,2 > =<6 0,3 6,9+ 2 > =<6,9,11 >

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Step 3

(b)

...
4u v42,1,3 > -0,3,1 >
= < 4 x 2,4 x 1,4 x 3 > -< 0,3,1>
=< 8,4,12 > < 0,3,1 >
=<8 0,4
3,12 - 1 >
=< 8,1,11 >
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4u v42,1,3 > -0,3,1 > = < 4 x 2,4 x 1,4 x 3 > -< 0,3,1> =< 8,4,12 > < 0,3,1 > =<8 0,4 3,12 - 1 > =< 8,1,11 >

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Math

Calculus