Show that the area of the triangle contained between the vectors a and b is one half of the magnitude of `a × b`.

Show that the area of the triangle contained between the vectors veca and vecb is one half of the magnitude of vecaxxvecb .

The vectors a,b and a+b are

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

The resultant of the vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between vecA" and "vecB is :-

Assertion: A vector quantity is a quantity that has both magnitude and a direction and obeys the triangle law of addition or equivalent the parallelogram law of addition. Reason: The magnitude of the resultant vector of two given vectors can never be less than the magnitude of any of the given vector.

Show that the median of a triangle divides it into two triangles of equal areas.

Find the area of the triangle formed by the tips of the vectors vec(a) = hati - hatj - 3hatk, vec(b) = 4hati - 3hatj +hatk and vec(c) = 3 hati - hatj +2 hatk .

If the area of the triangle formed by the points (2a,b), (a+b, 2b+a) and (2b, 2a) be Delta_(1) and the area of the triangle whose vertices are (a+b, a-b), (3b-a, b+3a) and (3a-b, 3b-a) be Delta_(2) , then the value of Delta_(2)//Delta_(1) is