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1.) A rigid body is rotating at 2.5 rad/sec about an axis AB,where A and B are the point (1,-2,1) and (3,-4,2). Find the velocity of the particle P of the body at the point(5,-1,-1). ? ^ ^ ^ ? ^ ^ ^ ? ^ ^ ^ 2.)If a=i+j-2k,ß=-i2j+3k, y=5i+0j+8k, then determine the scalars c and d ? ? ? such that y-ca-dß is perpendicular to both a and ß. ? 3.)If r=a cost i +a sint j+at tan ak,then ? ? find values of |(dr/dt)*(d²r/dt²)| ? ? ? and(dr/dt)*(d²r/dt²)*(d^3r/dt^3). 4.)Find the equations of the tangent plane and normol line to the surface xyz=4 at the point i+2j+2k. 5.)prove that (?*B dv= (n*B ds. v s

1.) A rigid body is rotating at 2.5 rad/sec about an axis AB,where A and B are the point (1,-2,1) and (3,-4,2).
Find the velocity of the particle P of the body at the point(5,-1,-1).

? ^ ^ ^ ? ^ ^ ^ ? ^ ^ ^
2.)If a=i+j-2k,ß=-i2j+3k, y=5i+0j+8k,
then determine the scalars c and d
? ? ?
such that y-ca-dß is perpendicular to
both a and ß.

?
3.)If r=a cost i +a sint j+at tan ak,then
? ?
find values of |(dr/dt)*(d²r/dt²)|
? ? ?
and(dr/dt)*(d²r/dt²)*(d^3r/dt^3).

4.)Find the equations of the tangent plane and normol line to the surface xyz=4 at the point i+2j+2k.

5.)prove that (?*B dv= (n*B ds.
v s

Grade:

1 Answers

vikas askiitian expert
509 Points
10 years ago

for this problem we need a perpendicular distance from point (5,-1,-1) to the axis AB..

drs of line AB are 2i -2j +k

eq of AB can be written as

                 r = i -2j +k + k(2i -2j +k) .........................1

now find general point in this line ,then find drs of line through this point and (5,-1,-1)

since AB and this line are perpendicular so dot product of drs is 0..

now u will get value of k for find this general point and by distance formula find perpendicular

distance...let dis distance is r..

then velocity at this point=wr

 

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