Question

If the position vector of the points A, B, C, D are
$3 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } } - \hat { \mathrm { k } }$ , $2 \hat { \mathrm { i } } + 3 \hat { \mathrm { j } } - 4 \hat { \mathrm { k } }$ , – ,

$4 \hat { \mathrm { i } } + 5 \hat { \mathrm { j } } + \lambda \hat { \mathrm { k } }$ respectively. If the points A, B, C, D lie on a plane then the value of l equals-

• A. $\frac { - 146 } { 17 }$
• B. $\frac { 146 } { 17 }$
• C. $\frac { 17 } { 146 }$
• D. $\frac { - 17 } { 146 }$

Answer 1

Answer: (A)

$\frac { - 146 } { 17 }$

Answer 2

If the points are coplanar then their P.V., $\overrightarrow { \mathrm { b } }$ ,, must satisfy the condition [ $\overrightarrow { \mathrm { b } }$ –,–,–]=0

̃ $\left| \begin{array} { c c c } - 1 & 5 & - 3 \\ - 4 & 3 & 3 \\ 1 & 7 & \lambda + 1 \end{array} \right|$= 0 ̃ l = – $\frac { 146 } { 17 }$