Let us recall that a vector product u * v is another vector (not a number!) dete

ID: 2834927 • Letter: L

Question

Let us recall that a vector product u * v is another vector (not a number!) determined by

three conditions: it is perpendicular to both u and v, it has magnitude that of the area of the

parallelogram formed by the two vectors, and it points in the direction described by the rule

of the right hand thumb (see Figure 11.56).

(a) Find the area of the triangle formed by three vertices: P(1, 0, 0);Q(0, 1, 2);R(-1, 0, 3).

(b) Is the vector i * (i + j) aligned with the direction of the z-axis or opposite to it?

P=(1, 0, 0);

Q=(0, 1, 2);

R=(-1, 0, 3).

so vector PQ= 1 i - j -2k
vector PR = 2 i + 0 j -3k
so area = 1/2 | PQ X PR| = 0.5 | 3i -1 j +2 k| = 1.87 sq units

(b) i X( i+j) = 0+ k = in the direction of z

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