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1. Given that ABCD is a parallelogram and A(1,1,0) B(-1,-1,-1) C(2,2,0) then what are the co-ordinates of D ? Also find the area of parallelogram ABCD ?

2. A triangle has 2 sides of length 5 and 6. The triangle's area is 12 .What is the angle between these two sides ?

3. Given the points A=(1,0,1) and B(1,1,1) and C(1,6,a) determine : (a) For what values of z are the points collinear ? (b) Determine if value exists for a so that A, B, c are three vertices of a parallelogram of area 3. If the value exists determine the co-ordinates of C ?

Note by Gaurav Sharma
3 years, 4 months ago

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1. Find the mid point of AC (diagnol) and then apply section formula (here mid point formula) on BD as it is also the mid point of BD. Because in ||gm Diagnols bisect each other.

2.Area of triangle when two sides and angle contained between the sides are given is $$\frac{1}{2}ABsin\theta$$ A and B are the lengths of sides.

$$\frac{1}{2}5.6sin\theta$$=12.

$$sin\theta$$=4/5

$$\theta$$=53 degrees

- 3 years, 4 months ago

3 one is lengthy thats why i m not writin that BUT 3 part is deeply same as 1 st part.

- 3 years, 4 months ago

Thanks !!

- 3 years, 4 months ago