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Let and F Be Sufficiently Smooth Scalar and Vector Fields

Question 35

Multiple Choice

Let Let and F be sufficiently smooth scalar and vector fields, respectively.Express the well-known identity . ( F ) = ( ) . F + ( . F) using the notations grad , div or curl. A) curl ( F) = grad ( ) . F + div (F) B) div ( F) = curl ( ) . F + grad (F) C) div ( F) = grad ( ) . F + div (F) D) grad ( F) = div ( ) . F + curl (F) E) curl ( F) = div ( ) . F + grad (F) and F be sufficiently smooth scalar and vector fields, respectively.Express the well-known identity Let and F be sufficiently smooth scalar and vector fields, respectively.Express the well-known identity . ( F ) = ( ) . F + ( . F) using the notations grad , div or curl. A) curl ( F) = grad ( ) . F + div (F) B) div ( F) = curl ( ) . F + grad (F) C) div ( F) = grad ( ) . F + div (F) D) grad ( F) = div ( ) . F + curl (F) E) curl ( F) = div ( ) . F + grad (F) . (11ee7bad_9f85_f900_ae82_29e1b84eee54_TB9661_11 F ) = (11ee7bad_7817_372f_ae82_a36163e56c30_TB9661_11 11ee7bad_9f85_f900_ae82_29e1b84eee54_TB9661_11 ) . F + 11ee7bad_9f85_f900_ae82_29e1b84eee54_TB9661_11 (11ee7bad_7817_372f_ae82_a36163e56c30_TB9661_11. F) using the notations grad , div or curl.

A) curl (11ee7bad_9f85_f900_ae82_29e1b84eee54_TB9661_11 F) = grad (11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 ) . F + 11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 div (F)
B) div (11ee7bad_9f85_f900_ae82_29e1b84eee54_TB9661_11 F) = curl (11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 ) . F + 11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 grad (F)
C) div (11ee7bad_9f85_f900_ae82_29e1b84eee54_TB9661_11 F) = grad (11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 ) . F + 11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 div (F)
D) grad (11ee7bad_9f85_f900_ae82_29e1b84eee54_TB9661_11 F) = div (11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 ) . F + 11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 curl (F)
E) curl (11ee7bad_9f85_f900_ae82_29e1b84eee54_TB9661_11 F) = div (11ee7bad_e8b4_1a82_ae82_cd578f612ee6_TB9661_11 ) . F + 11ee7bad_d4f5_2c01_ae82_0ffef783bd40_TB9661_11 grad (F)

Correct Answer: