Question

Let vectors \bar{A} =(2,1,-4), \bar{B} =(-3,0,1), \text{ and } \bar{C} =(-1,-1,2) Calculate the following: A)\bar{A} \cdot \bar{B}? E)Which of the fol

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ANSWERED
asked 2021-06-03
Let vectors \(\bar{A} =(2,1,-4), \bar{B} =(-3,0,1), \text{ and } \bar{C} =(-1,-1,2)\)
Calculate the following:
A)\(\bar{A} \cdot \bar{B}\)?
E)Which of the following can be computed?
\(\bar{A} \cdot \bar{B} \cdot \bar{C}\)
\(\bar{A}(\bar{B} \cdot \bar{C})\)
\(\bar{A}(\bar{B} + \bar{C})\)
\(3\bar{A}\)
F)Express your answer in terms of \(v_1\)
G) If \(v_1 \text{ and } v_2\) are perpendicular?
H) If \(v_1 \text{ and } v_2\) are parallel?

Answers (2)

2021-06-04
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Best answer
2021-09-08

A) \(\overline{A}=<2,1,-4>\ \overline{B}=<-3,0,1>\ \overline{C}=<-1,-1,2>\)

\(\overline{A}\cdot\overline{B}=<2,1,-4>\cdot<-3,0,1>=-6+0-4=-10\)

E) \(\overline{A}\cdot\overline{B}\cdot\overline{C}\) or \(\overline{A}(\overline{B}\cdot\overline{C})\) or \(3\overline{A}\) can not be computed because \((\overline{B}\cdot\overline{C})\) is a scalar quatitty as well as 3 and dot product is always belween 2 vectors.

\(\overline{A}\cdot(\overline{B}+\overline{C})\) can be computed

Since \((\overline{B}+\overline{C})\) is another vector dot product can be taken with \(\overline{A}\) and \((\overline{B}+\overline{C})\)

F) \(\overline{v_1},\overline{v_2}\)

\(\overline{v_1}\cdot\overline{v_1}=v_1^2\)

G) \(\overline{v_1}\) and \(\overline{v_2}\) are perpendicular

\(\overline{v_1}\cdot\overline{v_2}=v_1v_2\cos90^\circ=0\)

\(\overline{v_1}\cdot\overline{v_1}=v_1v_1\cos0^\circ=v_1^2\)

of \(\overline{v_1}\) and \(\overline{v_2}\) are parallel

\(\overline{v_1}\cdot\overline{v_2}=v_1v_2\cos0^\circ=v_1\cdot v_2\)

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