Question

A vector u with |u| = 7 points north and a vector v with |v| = 4 points northeast. The crossproduct (u x v) points:

A) south
B) northwest
C) up
D) down

and what is The magnitude |u x v| ?

Answer 1

The cross product of vectors u and v will have a magnitude of approximately 39.60.

Step-by-step explanation:

When we take the cross product of two vectors, the resulting vector points in a direction perpendicular to both of the original vectors. The magnitude of the cross product is given by the product of the magnitudes of the two vectors and the sine of the angle between them.

In this case, vector u points north and vector v points northeast. Since northeast is 45 degrees between north and east, the angle between u and v is 45 degrees.

The cross product (u x v) will have a magnitude of |u| * |v| * sin(angle) = 7 * 4 * sin(45) = 28 * sqrt(2) ≈ 39.60.

Therefore, the magnitude of the cross product is approximately 39.60.