MTH301 GDB Solution


MTH301 GDB Solution  

solution :
xi+ yj+ zk= (4cos3t)i +(4sin3t)j +(7t)k
r(t)= (4cos3t)i +(4sin3t)j +(7t)
r'(t)= (-12sin3t)i + (12cos3t)j + 7k
find at t= π / 4
r(π / 4) = ( 4cos3π / 4)i + (4sin3π / 4)j + (7π / 4)k
r(π / 4) = (4(-√2/2))i + (4(√2/2))j + (7π / 4)k
r(π / 4) = (-2√2)i + (2√2)j + (7π / 4)k
r'(π / 4) = (-12sin3t)i + (12cos3t)j + 7k
r'(π / 4) = (-12sin3π / 4)i + (12 cos3π / 4)j + 7k
r'(π / 4) = (-12(√2/2))i + (12(-√2/2))j + 7k
r'(π / 4) =(-6√2)i + (-6√2)j + 7k
 r'(π / 4) = -6(√2)i -6(√2)j + 7k
Vector equation of tangent line is as follows:
r = r(π / 4) + tr'(π / 4)
r = [(-2√2)i + (2√2)j + (7π / 4)k] + t[ -6(√2)i -6(√2)j + 7k]
r = (-2√2 - 6√2t)i + (2√2 - 6√2t)j + (7π / 4 + 7t)k
x = -2√2 - 6√2t
y = 2√2 - 6√2t
z = 7π / 4 + 7t



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