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Analytic Geometry Answers


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A ̅=5i+7j+8k

B ̅= 5i+2j-5k

Use your understanding of vector analysis to complete the following:

Calculate a resultant vector which would theoretically represent a single force that could replace the two force vectors A and B while giving the same support to the structure.

Calculate the modulus of all three forces.
Determine the value of the dot-product (scalar product) of vectors A and B
Calculate the angle between the vectors A and B
Determine the directional cosine angles of the resultant vector with respect to the x, y and z axes.
Find the equation of circle with center at the origin and tangent to the line 2x - 5y =8.
Find the standard form of the equation of circle whose center is at (4,3) which passes through the origin. Draw the circle
Identify an axis of revolution and generating conic of the surface 4x^2+25y^2+4z^2=100 . Does this conic also generates( x^2/4) +(y^2/25) + (z^2/4)=1 ? Give reason for your answer?
A rotating liquid forms a surface in the form of a paraboloid . The surface is 2m deep at the centre and 10 m across.Obtain an equation of the surface?
Which of the following statement are True? 1. x+y+z =0 touches the cone x ^2 + y^2+ z^2 +2(yz+zx+xy) =0 ?
The verticles of triangle ABC are: A(-2, -2), B(-5,-4),C(4,1). Round your answer to the nearest tenth.

a. Find the perimeter of the triangle

B. Find the area of the triangle

C. Johnathon says the triangle is a right triangle.
Do you agree or disagree. Why or why not ?
Angle between the lines x+3=0 and y+7=0
Write the equation for the hyperbola with foci (6,-5),(-4,-5) and conjugate axis of length 8?
Check whether or not the conicoid represented by 5x^2+4y^2-4yz+2xz+2x-4y-8z+2=0 is central or not.If it is,transform the equation by shifting the origin to the centre.Else,change any one coefficient to make the equation that of a central conicoid.