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

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?
\(\bar{A} \cdot \bar{B} \cdot \bar{C}\)
\(\bar{A}(\bar{B} \cdot \bar{C})\)
\(\bar{A}(\bar{B} + \bar{C})\)
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)

Best answer

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


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) \(\overline{v_1},\overline{v_2}\)


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



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

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


expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-06-10
Find an equation for the plane containing the two (parallel) lines
and \(v_2=(2,-1,0)+t(2,3,-1).\)
asked 2021-06-06
Let vectors \(A'=(2,\ 1,\ -4)\)
\(B'=(-3,\ 0,\ 1)\)
and \(C'=(-1,\ -1,\ 2)\)
Calculate the following:
asked 2021-05-16
Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.
asked 2021-05-29
Which of the following expressions are meaningful? Which are meaningless? Explain.
a) \((a\cdot b)\cdot c\)
\((a\cdot b)\cdot c\) has ? because it is the dot product of ?.
b) \((a\cdot b)c\)
\((a\cdot b)c\) has ? because it is a scalar multiple of ?.
c) \(|a|(b\cdot c)\)
\(|a|(b\cdot c)\) has ? because it is the product of ?.
d) \(a\cdot(b+c)\)
\(a\cdot(b+c)\) has ? because it is the dot product of ?.
e) \(a\cdot b+c\)
\(a\cdot b+c\) has ? because it is the sum of ?.
f) \(|a|\cdot(b+c)\)
\(|a|\cdot(b+c)\) has ? because it is the dot product of ?.