Question

If $\overrightarrow { \mathrm { a } } _ { 1 } , \overrightarrow { \mathrm { a } } _ { 2 } , \overrightarrow { \mathrm { a } } _ { 3 }$ are non-coplanar vectors and

(x + y – 3) $\overrightarrow { \mathrm { a } } _ { 1 }$ + (2x – y + 2) $\overrightarrow { \mathrm { a } } _ { 2 }$ + (2x + y + l)holds for some ‘x’ and ‘y’ then l is

• A. $\frac { 7 } { 3 }$
• B. 2
• C. $- \frac { 10 } { 3 }$
• D. $\frac { 5 } { 3 }$

Answer 1

Answer: (C)

$- \frac { 10 } { 3 }$

Answer 2

Since $\overrightarrow { \mathrm { a } } _ { 1 } , \overrightarrow { \mathrm { a } } _ { 2 } , \overrightarrow { \mathrm { a } } _ { 3 }$ are non-coplanar vectors

\ x + y – 3 = 0 .....(2x – y + 2 = 0 .....(ii)

2x + y + l = 0 .....(iii) From (i) and (ii) x = 1/3, y = 8/3 \

from (iii) l = – $\frac { 10 } { 3 }$