: Consider the vectors, u =(2, – 4), v = (4, 2), and w = v – u.
(a) Find the magnitude, and the direction of the vectors, u, v, and w.
(b) Find the area, A, of the triangle, T, the three sides of which are made by the vectors, u, v and w. What kind of triangle is T?
(c) Find the volume of the prism the length of which is, l = 6, and the cross-section of which is the triangle made by the vectors, u and v.
Can you helpe with this question regarding vectors ?
This is easily dealt with by sketching on graph paper. The area is half the sum of the three determinants
| xu yu |, | xv yv |, | xw yw |
| xv yv |. | xw yw |. |xu yu |
and the volume of the prism will six times that.
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