Question

Obtain an expression for the area of a triangle in terms of cross product of two vectors representing the two sides of triangle
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If u know the answer than reply only​

Answer 1

Answer:

yes l know the answer

Explanation:

half half into base into height

Answer 2

An expression for the area of a triangle in terms of the cross product of two vectors representing the two sides of a triangle is 1/2 × | A X B |

Given: The two sides of the triangle.

To Find: An expression for the area of a triangle in terms of the cross product of two vectors representing the two sides of the triangle.

Solution:

Suppose we take a triangle ABC where the side BA is represented by vector B and side BC by vector A.

Now, we know that the area of a triangle is,

        Area = 1/2 × base × height                     .........(1)

Now, we are given the cross product of the two vectors,

        Cross product = | A X B |                      

We also know that,

        | A X B |  = | A | × | B | × sin Ф                   ...........(2)

where Ф = angle between the two vectors A and B.

We can visualize that the height of the triangle may be represented by,

       Height = | B |× sin Ф                                   ...........(3)

and   Base = | A |                                                ...........(4)

So putting (3) and (4) in (1), we get;

       Area = 1/2 × base × height

                = 1/2 × | A | × | B | × sin Ф

From (2), we can conclude that,

       Area = 1/2 × | A X B |

Hence,

An expression for the area of a triangle in terms of the cross product of two vectors representing the two sides of a triangle is 1/2 × | A X B |

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