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Proof
1)d=nA+mB implies (A×B).d=0
2) A×C=B×C implies C.A-C.B=C|A-B|
("×"cross product ("." Dot product)
Find the equation (formula) of a sphere with radius r and center C(h, k, l) and show that x2 + y2 + z2 - 6x + 2y + 8z - 4 = 0 is an equation of a sphere. Also, find its center and radius
A cow is tied to one of the corners of the square field who side is 55 meters long.If the length of the rope is a tenth of the side field, what is the area of the field that is not grazed in cm2?
Let F be the R²-R function defined by f(x,y)=(x-y)³.
1.determine the rate of increase in f at the point (2,1) in the direction of the vector(1,-1).then use theorem.
2.what is the rate of increase in f at (2,1) in the direction of the negative x-axis?
3.determine the maximum rate of increase in f at (2,1). In which direction is the maximum rate of increase? (read corollaries).
Calculate the equation for the plane containing the lines L1 and L2,where L1 is given by the parametric equation (x,y,z)=(1,0,-1)+t(1,1,1),t€R and L2 is given by the parametric equation (x,y,z)=(2,1,0)+t(1,-1,0),t€R.
A 9N force F1 and a 10N force F2 act in the same direction 2i+j-2k and 4i-3j respectively.
a) Find the resultant of the two forces
b)find the total work done if the forces make the object move 2m along the vector S=i+j+k
c)what is the maximum work done that can be achieve if the forces displace the object by 1m?
d)what is unit vector along which the object will move to achieve maximum work done?
f) find F1.F2
g) find F1*F2
Given that A = 2i + 3j - k, B = i - j +2k and C = 3i + 4j + k
a)find the unit vector along the direction of nA, for n<0
b) find the length of the projection of vector A on vector C
c)find the length of projection of vector C and vector A
d) find the sine of the angle between vector A and vector C
Show that X^2 + Y^2 + Dx + Ey + F=0 represents a circle of positive radius if and only if D^2 + E^2 - 4F > 0.
Show that vector A and vector BB are parallel (both in same and different directions), then each can be expressed as a multiple of the other
Find the vector C of magnitude c that is perpendicular to vectors A=a1i + a2j + a3k and B=b1i + b2j + b3k
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#340153 on Dec 2023