Anthony has added the vectors listed below and gotten the result $\overrightarrow { \mathbf { R } } = 9 \hat { \mathbf { i } } + 4 \hat { \mathbf { j } } + 6 \hat { \mathbf { k } }$ .What errors has he made? $\overrightarrow { \mathbf { A } } = 3 \tilde { \mathbf { i } } + 4 \tilde{ \mathbf { j } } - 5 \tilde { \mathbf { k } }$ $\overrightarrow { \mathbf { B } } = - 3 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } } + 8 \hat { \mathbf { k } }$ $\overrightarrow { \mathbf { C } } = 3 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } } + 2 \hat { \mathbf { k } }$
A)He lost the minus sign in vector $\vec { B }$ .
B)He read the $2 \tilde { \mathbf { k } }$ in $\overrightarrow { \mathrm { C } }$ as $3 \tilde { \mathbf { k } }$ .
C)He lost the minus sign in vector $\overrightarrow { \mathrm { A } }$ .
D)All of the above are correct.
E)Only (a)and (b)above are correct.

Question

Quizplus · Accepted Answer

In each vector, there are 9 occurrences of "TB5764_11". Therefore, their sum should have "TB5764_11" occurring 9 times as well. However, the given result has "TB5764_11" occurring 8 times only. This means that the vector with the error has "TB5764_11" occurring one time less than it should have. This error occurs only in vectors (a) and (b), where the 3rd to the last element is "4702b3cd100f" and "f7f199a5b10e", respectively, instead of "8bb6" as in all other vectors. Therefore, the error is in subtracting these two vectors, resulting in a difference of "8bb6 - 4702b3cd100f = 8bb6 + b8fdbcc2ef01" which was added to the sum instead of subtracted. This explains errors (a) and (b) only, and the correct answer is (E).

Anthony Has Added the Vectors Listed Below and Gotten the Result