Find the volume of a parallelepiped
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- (b) Find the area of the triangle whose vertices: are A(0,0,0) ; B(1,1,1) and C(0,2,3).1- In space ,the point can be specified by position vector r wnich is given by: A:r-ix+ jy c r=ix+ jy + kz B:r=ix+ D:r=ix3- Two vectors A-i+2}-k written . A: 12 and lying in the xy-plane, the A.B can be В: 10 C: 6 D. 0
- 3) From elementary geometry we know that there is a unique straight line through any two points in a plane. Less well known is the fact that there is a unique parabola through any three non- collinear points in a plane. For each set points below, find a parabola with an equation of the form y= ax2+bx+c that passes through the given points. a) (0, 1), (-1, 4), and (2, 1)9. The line segment joining A(4, 1) and B(-2,5) is extended to point C through B. Find the coordinates of C if B is the midpoint of AC. A) (-5,7) B) (-8,9) C) (-6,8) D) (-7,10)A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what distance d will kx for the new region be the same as kx (for the region before the cutout was removed?
- 1. Find the components of . 2. A Find the components of T2- (Reminder: cos(a) =) 3. Find the angle between and 2. 4. Find the magnitude of the projection of r2 along/parallel to T = 6m 30° 40° Z 8 60° r₁= r₂ = √2 120° 45⁰ a 0 = Y= 2 = 9 m optional1. If A(-4,–6), B(3,–3), C(5,7), and D(x.,y) are vertices of a parallelogram ABCDA, determine the coordinates of D. C) (-3,5) D) (-2,4) A) (-2,5) B) (-3,4)Use De Moivre's theorem to (i) express (2 + 2i)5 in polar form. (ii) find all cube roots of (V3 + i) in polar form.
- Fill in the blanks in the following: 1. The vectors A and Bare parallel if A.B = ..........or A x B= 2. If (9,5,-4, 2) and = (-3, -2, 7,-1) the .=. 3. If a= (-8, 2) and b=(-1,-7) the projection on to a = …………………. *******4. Use Geogebra and the Klein-Beltrami model to show that a pentagon with five right angles and a hexagon with six right angles can be drawn in hyperbolic geometry. Hint: Start with two lines that have a common perpendicular.Find the poles of those two lines, then draw an appropriate line through each pole, so on.For the four noded element with coordinates (2,1), (5,0), (5.5,2.5) and (4,3) determine the jacobian matrix