Given that $\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } } = x _ { 2 } \hat { \mathbf { i } } + y _ { 2 } \hat { \mathbf { j } }$ ,what is $\overrightarrow { \mathrm { A } }$ ?
A) $\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } - x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 2 } \left( y _ { 1 } - y _ { 2 } \right) \hat { \mathbf { j } }$
B) $\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } + x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 2 } \left( y _ { 1 } - y _ { 2 } \right) \hat { \mathbf { j } }$
C) $\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } - x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 2 } \left( y _ { 1 } + y _ { 2 } \right) \hat { \mathbf { j } }$
D) $\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } + x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 2 } \left( y _ { 1 } + y _ { 2 } \right) \hat { \mathbf { j } }$
E) $\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } + x _ { 2 } \right) \hat { \mathbf { i } }$

Question

Quizplus · Accepted Answer

To solve this problem, we need to compare the given strings and find the pattern between them. The first part of the string "11ea99f6_d75e" is common in both given strings. The third set of characters are changing in both strings. In the first string, it is "7e82", and in the second string, it is "7e83". The last set of characters are the same in both strings, and it is repeating eight times in each.
Now, coming to the answer string, we need to find the pattern in the third set of characters. By observing the first two strings, we can see that the third set of characters is increasing by one in each string. So, the next one should be "a593" (which is "a594" - 1) to follow the pattern. Therefore, the correct answer is D) 11ea99f6_d75e_a598_8bb6_a9a8b6a000de_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11.

Given That A→+B→=x1i^+y1j^\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }A+B=x1​i^+y1​j^​

Given That $\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }$