1) calculate the are of the parallelogram defined by the vectors =+2v , b= - v w

Question

1) calculate the are of the parallelogram defined by the vectors =+2v , b= - v where =[1,1,1], v=[2,1,1]

2) find parallel (i.e. ||) and normal (i.e. ) component of the vector =d^2r(0)/dt^2 in the direction of the vector v=dr (0)/dt for 3cos(2t)I +3sin (2t)j + (t+1)^2k

3) find the equation of the plane passing through three points A=(1,1,2),B=(2,3,5)C=(1,2,0). Is the plane -7x + 2y + z + 1= 0 parallel to the plane?

4) write the equation of the following like {x - 2= 2y -2 , 2y -2= 4z -4 in the parametric form. Is the like x-1/4 = y-2/2 =z-1/1 parallel to that line?

5)calculate the normal component of acceleration (i.e an =Kv^2) for r= cos (t^2/2)i +sin (t^2/2)j +2k

11 s nC throu tres ports 11of the plane cass ng throuzr tre: poi%SA-1,2,2. 6-2. Ti iApt020ralicl 101ha:Dan:7 a- tion of the rcllowing ane 2-1:-4 paalel to that ine?

Explanation / Answer

1)   a = u +2v = (1 , 1,1) + 2(2,1,1) = ( 5 , 3 , 3) ; b = u - v = ( 1,1,1) - ( 2, 1,1) = ( -1 ,0,0)

Area of Parallelogram = | u x w| = | ( 0 , -3 , 3) | = sqrt( 3^2 + 3^2) = 3sqrt2 sq.units

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