Find the unit tangent vector for at
A) i j k
C) i + j + k

Question

Find the unit tangent vector  for  at 
A) i j k 
C) i + j + k

Quizplus · Accepted Answer

To find the unit tangent vector, we need to differentiate the given position vector with respect to the parameter and then divide it by its magnitude. The position vector is given as 11eaa3e5_54f8_c8e3_9f8f_4d8112d0556b_TB5971_11, so its derivative with respect to the parameter is the vector connecting 11eaa3e5_54f8_c8e4_9f8f_7fa2d499f2f2_TB5971_11 and 11eaa3e5_54f8_c8e3_9f8f_4d8112d0556b_TB5971_11. This vector is (11eaa3e5_54f8_c8e4_9f8f_7fa2d499f2f2_TB5971_11 - 11eaa3e5_54f8_c8e3_9f8f_4d8112d0556b_TB5971_11) = 11eaa3e5_54f8_eff9_9f8f_8fb475c3bedc_TB5971_11 i + 11eaa3e5_54f8_effa_9f8f_37982f91ff5f_TB5971_11 j + 11eaa3e5_54f8_effb_9f8f_316251a8e4a5_TB5971_11 k. The magnitude of this vector is sqrt(3), so the unit tangent vector is (1/sqrt(3)) times this vector, which is 11eaa3e5_54f8_eff9_9f8f_8fb475c3bedc_TB5971_11 i + 11eaa3e5_54f8_effa_9f8f_37982f91ff5f_TB5971_11 j + 11eaa3e5_54f8_effb_9f8f_316251a8e4a5_TB5971_11 k. Therefore, the correct answer is C.

Find the Unit Tangent Vector for at