Question

The three vectors $\overset{\hat{}}{i}$+ 2 +$\overset{\hat{}}{j}$+$\overset{\hat{}}{k}$ , a$\overset{\hat{}}{i}$+$\overset{\hat{}}{j}$ + 2$\overset{\hat{}}{k}$ and

$\overset{\hat{}}{i}$+ 2$\overset{\hat{}}{j}$ + a$\overset{\hat{}}{k}$ are coplanar-

• A. For no real value of a
• B. For all real values of a
• C. For one real value of a
• D. For two real values of a

Answer 1

Answer: (D)

For two real values of a

Answer 2

Condition for coplanarity is $\left| \begin{matrix} 1 & 2 & 1 \\ a & 1 & 2 \\ 1 & 2 & a \end{matrix} \right|$= 0 which gives

2a2 – 3a + 1 º (2a – 1) (a – 1) = 0 or a = $\frac{1}{2}$ and 1.