Vectors

posted by samantha

The person who helped me before was not very helpful.

ABC has vertices A(3,2,-5), B(4,-1,7) and C(-8,3,-6).

a) Determine the area of ABC.

b) Determine the coordinates of point D such that ABCD is a parallelogram.

1. Steve

Given two vectors u and v, forming two sides of a parallelogram, u+v is the corner opposite (0,0). Here, we can take

u = B-A = (1,-3,12)
v = C-A = (11,1,-1)

The area of ∆ (not ) ABC is half the area of the parallelogram ABCD. So, it is

1/2 |uxv| = 1/2 |(-9,133,34)| = 1/2 √18926 = 68.79

The parallelogram is not a rectangle since

uv = 11-3-12 = -4 ≠ 0

Similar Questions

1. Math

A(-11,8)B(2,-6) and C(-19,-8) are the vertices of Triangle ABC. N(X,Y) is a point on AC such the BN is Perpendicular to AC. Find Area of Triangle ABC. PLEASE HELP!!!
2. chemistry

(i) Explain why the freshman criterion for sponteneity: G=H-TS < 0 is just a statement of the second law of thermodynamics (that the entropy of the universe always increases). Now apply this concept to some …
3. geometry

The vertices of ABC are A(-8, 0), B(0, 0), and C(0, -4). If a circle is circumscribed around ABC, where would the center of the circle be located?
4. geometry

The vertices of ABC are A(-8, 0), B(0, 0), and C(0, -4). If a circle is circumscribed around ABC, where would the center of the circle be located?
5. geometry

Triangle ABC with an area of 243 cm2 is similar to WXY. If BD = 18 cm and XZ = 4 cm, what is the length of segment WY?
6. chem 3

(a) If H is positive and S is negative, would G to be positive or negative or is it dependent on T?
7. calculus 12

7. ABC has vertices A(3,2,-5), B(4,-1,7) and C(-8,3,-6). a) Determine the area of ABC. b) Determine the coordinates of point D such that ABCD is a parallelogram. c) Is the parallelogram a rectangle?
8. Chem

I am still having problems this question 2. Review Examples 7.3 and 7.4, as well as the equation for E in the chapter notes. Suppose an e−1 in an H atom has a transition from n = 3 to n = 2. a. Determine the energy (E) …
9. chemistry

17. Calculate H for the following reaction using Hess law H2 (g) + Br2 (g) → 2 HBr (g) Experimental information 2 H+ → H2 H -436.4 kJ 2 Br- → Br2 H -192.5 kJ 2 H+ + 2 Br- →2 HBr H …
10. Geometry

The coordinates of the vertices of ABC are A(-2,2) B (5, -3) and C (-4,-1) Identify the perimeter of ABC. Round each length to the nearest tenth before adding. I am totally lost!

More Similar Questions