The area of a triangle formed by two vectors u and v can be found using the formula for the cross product of two vectors. The cross product of two vectors gives a vector that is perpendicular to the plane of the two vectors, and its magnitude is equal to the area of the parallelogram formed by the two vectors. Since a triangle is half of a parallelogram, we divide the magnitude of the cross product by 2 to get the area of the triangle.

Here are the steps:

1. First, find the cross product of the two vectors u and v. The cross product of two vectors u = (u1, u2, u3) and v = (v1, v2, v3) is given by w = u x v = (u2v3 - u3v2)i - (u1v3 - u3v1)j + (u1v2 - u2v1)k.

2. Then, find the magnitude of the cross product vector w. The magnitude of a vector w = (w1, w2, w3) is given by |w| = sqrt(w1^2 + w2^

Question

The area of a triangle formed by two vectors u and v can be found using the formula for the cross product of two vectors. The cross product of two vectors gives a vector that is perpendicular to the plane of the two vectors, and its magnitude is equal to the area of the parallelogram formed by the two vectors. Since a triangle is half of a parallelogram, we divide the magnitude of the cross product by 2 to get the area of the triangle.

Here are the steps:

1. First, find the cross product of the two vectors u and v. The cross product of two vectors u = (u1, u2, u3) and v = (v1, v2, v3) is given by w = u x v = (u2v3 - u3v2)i - (u1v3 - u3v1)j + (u1v2 - u2v1)k.

2. Then, find the magnitude of the cross product vector w. The magnitude of a vector w = (w1, w2, w3) is given by |w| = sqrt(w1^2 + w2^

Knowee AI · Accepted Answer

The area of a triangle formed by two vectors u and v can be found using the formula for the cross product of two vectors. The cross product of two vectors gives a vector that is perpendicular to the plane of the two vectors, and its magnitude is equal to the area of the parallelogram formed by the two vectors. Since a triangle is half of a parallelogram, we divide the magnitude of the cross product by 2 to get the area of the triangle.

Here are the steps:

1. First, find the cross product of the two vectors u and v. The cross product of two vectors u = (u1, u2, u3) and v = (v1, v2, v3) is given by w = u x v = (u2v3 - u3v2)i - (u1v3 - u3v1)j + (u1v2 - u2v1)k.

2. Then, find the magnitude of the cross product vector w. The magnitude of a vector w = (w1, w2, w3) is given by |w| = sqrt(w1^2 + w2^

u i j k v i j k and 2   w i j k .i. Find the area of a triangle that is formed by the two vectors u and v .

Question

Find the area of a triangle that is formed by the two vectors

Solution

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