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Mathematics: Post your doubts here!

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M2, s04, Q4 part 1.
According to the figure I can tell that the force in the rod is 0.7m from the hinge and has to act upward for equilibrium.
But mark scheme says ,

Distance of the rod from the hinge is (0.7) 2.4/2.5 or 0.7cos16.26° (=0.672). How did come to be? Please help!

Capture.PNG
 
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Hey! First question, to find the angle between the two planes we can find the angle between the two normals. That is equal to the angle between the two planes.
The first normal is i+j+3k and the second is 2i-2j+k. Using the dot product between these two we have: (1)(2)+(1)(-2)+(3)(1)=sqrt(1^2+1^2+3^2)*sqrt(2^2+2^2+1^2)cos(theta)
theta=72.5

Second question, before i proceed, do you know how use the vector product to find common perpendiculars or do you use another method?
 
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View attachment 63629
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Can anyone tell me how to shade the region?
and how to represent Re z >2
Help me Maths nerds.

Zaki ali asghar
Modulus of (z-u) being less than 2 is basically a circle with center u of radius 2 and the wanted region is whats inside the circle because its less than.
Re z>2 means real part must be bigger than 2 so the x value of the complex number on the argand diagram must be greater than 2 so draw the line x=2 and the final shaded region should be

The region inside the circle that is to the right of line x=2
 
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Hey! First question, to find the angle between the two planes we can find the angle between the two normals. That is equal to the angle between the two planes.
The first normal is i+j+3k and the second is 2i-2j+k. Using the dot product between these two we have: (1)(2)+(1)(-2)+(3)(1)=sqrt(1^2+1^2+3^2)*sqrt(2^2+2^2+1^2)cos(theta)
theta=72.5

Second question, before i proceed, do you know how use the vector product to find common perpendiculars or do you use another method?
Common perpendiculars??? finding the intersection line of these two planes(other method)
 
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Modulus of (z-u) being less than 2 is basically a circle with center u of radius 2 and the wanted region is whats inside the circle because its less than.
Re z>2 means real part must be bigger than 2 so the x value of the complex number on the argand diagram must be greater than 2 so draw the line x=2 and the final shaded region should be

The region inside the circle that is to the right of line x=2
Thanks for replying thanks a lot.
 
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How do we draw |z-5| =|z|
where |z|=5 is a circle with radius 5 and center at the origin.
I know that it's going to be a perpendicular bisector of the |z-5| line but is |z-5| a horizontal line along the x-axis with magnitude 5 and the perpendicular bisector at 2.5?
 
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How do we draw |z-5| =|z|
where |z|=5 is a circle with radius 5 and center at the origin.
I know that it's going to be a perpendicular bisector of the |z-5| line but is |z-5| a horizontal line along the x-axis with magnitude 5 and the perpendicular bisector at 2.5?
For this you have to plot 2 points
(5,0) and (0,0)
draw perpendicular bisector of these two points
Yes, it is at x=2.5
 
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