i. Find b × c in terms of λ . ii. Show that a · (b × c) is independent of λ .  iii. Find the volume of the tetrahedron and the area of OABC.

Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: The line of action of the 2690-lb force runs through the points A and B as shown in the figure.…

A: The slope: m of a line that passes through the points: x1, y1 and x2, y2 is calculated using the…

Q: Find the positive value for which the vector r(t) (2t, 9t?, 10t2 – 2) is perpendicular to r'(t). -

A:

Q: Find a parametrization for the line segment joining the points P(10,0,10) and Q(0,10,0). Draw…

A:

Q: Consider the following function. T: R² - R?, T(X, V) = (Vã, sxy, Vỹ) Find the following images for…

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Q: Let L₁ be the line parametrized by (4-2t, 2-t, 3+t). Let L₂ be the line parallel to L₁ going through…

A:

Q: 7. Jason has a trunk whose inside is 16 inches wide, 30 inches long and 12 inches high. Will a…

A: Given query is to find that telescope measuring 34 inch is going to fit inside the trunk or not.

Q: Consider the points A(2, –3, 4), B(4, –5, 1), C'(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of…

A:

Q: Use the diagram below to find the two angles. Be sure to show all of your work. axt15 3XF1O 3x+10

A: From the diagram we know that (2x+15)+(3x+10) = 180. So,             (2x+15)+(3x+10) = 180…

Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

A:

Q: Identify the surface by eliminating the parameters from the vector-value r(u.v) = 3 cosv cosui +3…

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Q: Consider the following function. T: R2 → R?, T(x, y) = (x, 5) Find the following images for vectors…

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Q: Let C be the curve with vector function 7(t) = (cos(vt), sin( Vt ), /3t ) for 0sts“,. 4 a) The…

A: Given that the curve C has a vector function r→t=cost,sint,3t for 0≤t≤π24. a) It is required to find…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.