Which of the following statements is always true for any vectors and ?

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

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