Question

What mistake did Kelcy make? She added (-4, 3) and (5, 1) incorrectly. She did not correctly distribute 3 to both components of u. She should have distributed -5 to both v and w before adding. She should have subtracted (27,-6) and (5,-20), rather than adding.

Answer 1

Kelcy's mistake involved incorrect vector addition, possibly due to a misapplication of the distributive property when combining vector components. She should have added or subtracted the corresponding components of each vector depending on the operation required by the question.

Step-by-step explanation:

From the information provided, the student Kelcy made a mistake in a problem involving vector addition. In vector addition, it is crucial to accurately combine the components of each vector. When Kelcy added the vectors (-4, 3) and (5, 1), it seems that she may have incorrectly applied the distributive property or may not have properly combined the vector components. Instead of distributing a scalar to both components of a vector, one should simply add or subtract the corresponding components of each vector. For instance, adding vectors (-4, 3) and (5, 1) should result in (1, 4) by adding the x-components (-4 + 5) and the y-components (3 + 1) separately.

When subtracting vectors as in the sailing example, we understand that subtraction of vectors is analogous to taking steps in reverse. If Kelcy was supposed to subtract the vectors (27,-6) and (5,-20), she should have taken the 'steps' in reverse by adding the opposite of the second vector, resulting in (27+(-5), -6-(-20)) = (22, 14). Instead, she appears to have incorrectly added when she should have subtracted.