Urgent problem！(Calculus)How to solution this problem？?

■■■■■Please give me detailed solution■■■■■


1.If vectorA=(1,0,3)，vectorB=(5,2,6)，findθAB=...


2.Show that vectors vector a=(4,0,-1),vector b=(1,3,4)，vector c=(-5,-3.-3)


form the sides of a triangle. Is this a right triangle?


Calculate the area of the triangle


3.(a)Convert points P(1,3,5),T(0,-4,3),and S(-3,-4,-10) from Cartesian to cylindrical


and spherical coordinates.


(b)Transform vector


vector Q= ( [√(x²+y²)/√(x²+y ²+z²)] , 0 , -yz/√(x²+y²+z²) )


to cylindrical and spherical coordinates


(c)evaluate vector Q at T in the three coordinate systems

Urgent problem！(Calculus)How to solution this problem？?
1. cosθ=A*B / (|A|*|B|)=(1*5+0*2+3*6) / 5√ 26


=81.171





2. assume the angle of vectors of a and b is "m"


so cos m= a*b/(|a|*|b|)=0 because cos90=0


m=90...so it is a right triangle...


|a| and |b| are representing the right-angled sides of the triangle.


|a|=√17; |b|=√26


S=|a|*|b| / 2 =10.5





3. P(1,3,5) to cylindrical coordinates.......


r=√1+9 =√10....


θ= tan^(-1)3=71.6


z= 5


In terms of x , y , and z


x= r.cosθ =√10*71.6 =226


y= r.sinθ = 0.95*√10= 3


z=5


so its (226,3,5)


ditto, T 's doesn't have cylindrical coordinates


S 's cylindrical coordinates is (0.6, -0.8, -10)


......................(that's all i know..)

garden centre