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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?

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?

asked 2021-05-19

Find the directional derivative of f at the given point in the direction indicated by the angle \(\theta. f(x,y)=e^x\cos y,(0,0),\theta=\frac{\pi}{4}\)

asked 2021-05-29

Find the directional derivative of f at the given point in the direction indicated by the angle theta. \(f(x,y)=ye^{-x}, (0,4), \theta=\frac{2\pi}{3}\)

asked 2021-05-06

A spring is mounted vertically on the floor. The mass of the spring is negligible. A certain object is placed on the spring to compress it. When the object is pushed further down by just a bit and then released, one up/down oscillation cycle occurs in 0.250 s. However, when the object is pushed down by 5.00 X 10^-2 m to point P and then released, the object flies entirely off the spring. To what height above point P does the object rise in the absence of air resistance?

asked 2021-05-27

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.

\(L1:\frac{x}{1}=\frac{y-1}{-1}=\frac{z-2}{3}\)

\(L2:\frac{x-2}{2}=\frac{y-3}{-2}=\frac{z}{7}\)

\(L1:\frac{x}{1}=\frac{y-1}{-1}=\frac{z-2}{3}\)

\(L2:\frac{x-2}{2}=\frac{y-3}{-2}=\frac{z}{7}\)

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 ?.

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 ?.

asked 2021-05-22

The function \(f(x)=4-7x^{4}\) has an absolute maximum value of ? and this occurs at x equals ?

asked 2021-05-18

1. S1 and S2, shown above, are thin parallel slits in an opaqueplate. A plane wave of wavelength λ is incident from the leftmoving in a direction perpendicular to the plate. On a screenfar from the slits there are maximums and minimums in intensity atvarious angles measured from the center line. As the angle isincreased from zero, the first minimum occurs at 3 degrees. Thenext minimum occurs at an angle of-

A. 4.5 degrees

B. 6 degrees

C. 7.5 degrees

D. 9 degrees

E. 12 degrees

asked 2021-05-25

Find a vector function that represents the curve of intersection of the two surfaces. The cylinder \(x^2+y^2=4\) and the surface z=xy

asked 2021-04-24

Find the second partial derivatives for the function \(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{{4}}}-{3}{x}^{{{2}}}{y}^{{{2}}}+{y}^{{{2}}}\) and evaluate it at the point(1,0).