Question

Given that the vectors $\overline{a},\overline{b},\overline{c}$ form a base, find the sum of co-ordinates of the vector: $3\overline{u}-\overline{v}+\overline{w}$

if $\overline{u}=\overline{a}+\overline{c},\overline{v}=\overline{b}+\overline{c},\overline{w}=\overline{a}-\overline{b}$;

• A. 4
• B. 6
• C. 2
• D. 3

Answer 1

Answer: (A)

4

Given vectors

$\overline{u}=\overline{a}+\overline{c}$

$\overline{v}=\overline{b}+\overline{c}$

$w=\overline{a}-\overline{b}$

$3\overline{u}-\overline{v}+\overline{w}=3(a+c)-(b+c)+(a-b)$

$=3a+3c-b-c+a-b$

$=4a-2b+2c$.

Sum of the co-ordinates of the vector

$=4+(-2)+2=4-2+2=4$.

$\therefore$ The given option is correct.