Obtain an expression for the area of a triangle in terms of the cross product of two vectors representing the two sides of the triangle

The area of a triangle is half the product of any of its sides and the corresponding altitude.

The area of a triangle formed by the sides of vector vec(A)and vec(B) is

If the ratio of the dot product of two vectors and cross product of same two vectors is sqrt3 , the two vectors make angle

Each of sides of a triangle is 8cm less than the sum of its other two sides.Area of the triangle ( in cm^(2)) is

The ratio of the area of two similar triangle is 4:5 , the ratio of their corresponding sides are :

Is it true to say that, if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reason for your answer.

Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.

If two sides and a median bisecting one of these sides of a triangle are respectively proportional to the two sides and corresponding median of another triangle; then triangle are similar.

Show,by vector methods,that the angularbisectors of a triangle are concurrent and find an expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.