Mathematics

Mathematics

Problem

Which of the following statements is always true for any vectors

\mathbf{a}=a_x\hat{i}+a_y\hat{j}+a_z\hat{k}

and

\mathbf{b}=b_x\hat{i}+b_y\hat{j}+b_z\hat{k}

? a) The

z

-component of

\mathbf a-\mathbf b

equals

b_z-a_z

. b) The

y

-component of

\mathbf a-\mathbf b

equals

a_y-b_y

. c)

|\mathbf a+\mathbf b|=|\mathbf a|+|\mathbf b|

. d) The

x

-component of

\mathbf a-\mathbf b

equals

a_x+b_x

.

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