Question

Given that =$\overrightarrow { \mathrm { i } }$ + , $\overrightarrow { \mathrm { e } _ { 2 } }$ = $\overrightarrow { \mathrm { i } }$ + $\overrightarrow { \mathrm { k } }$ ,

= + $\overrightarrow { \mathrm { k } }$ and if 5$\overrightarrow { \mathrm { i } }$ + 2 + $\overrightarrow { \mathrm { k } }$ = l1 + l2 $\overrightarrow { \mathrm { e } _ { 2 } }$ + l3, then (l1, l2, l3) is equal to

• A. (3, 2, 1)
• B. (3, 2, –1)
• C. (3, 3, –2)
• D. (3, ­–2, –1)

Answer 1

Answer: (B)

(3, 2, –1)

Answer 2

5 $\overrightarrow { \mathrm { i } }$+ 2+ $\overrightarrow { \mathrm { k } }$ = l1 ($\overrightarrow { \mathrm { i } }$+) + l2 ($\overrightarrow { \mathrm { i } }$+ $\overrightarrow { \mathrm { k } }$ ) + l3(+ $\overrightarrow { \mathrm { k } }$

= (l1 + l2) $\overrightarrow { \mathrm { i } }$ + (l1 + l3) + (l2 + l3) $\overrightarrow { \mathrm { k } }$

Adding l1 + l2 + l3 = 4

\ l1 = 3

l2 = 2

l3 = – 1