Question

The area of the triangle formed by the adjacent sides with is

• A. $\frac { \sqrt { 165 } } { 2 }$ units
• B. $\frac { \sqrt { 137 } } { 2 }$ units
• C. $\sqrt { 165 }$ units
• D. $\sqrt { 137 \text { units } }$

Answer 1

Answer: (A)

$\frac { \sqrt { 165 } } { 2 }$ units

Answer 2

$\overrightarrow { \mathrm { A } } \times \overrightarrow { \mathrm { B } } = \left| \begin{array} { c c c } \hat { \mathrm { i } } & \hat { \mathrm { j } } & \hat { \mathrm { k } } \\ - 3 & 2 & - 4 \\ - 1 & 2 & 1 \end{array} \right|$

$= \hat { \mathrm { i } } [ 2 + 8 ] + \hat { \mathrm { j } } [ 4 + 3 ] + \hat { \mathrm { k } } [ - 6 + 2 ]$

$= 10 \hat { \mathrm { i } } + 7 \hat { \mathrm { j } } = 4 \hat { \mathrm { k } }$

$\therefore | \overrightarrow { \mathrm { A } } \times \overrightarrow { \mathrm { B } } | = \sqrt { 10 ^ { 2 } + 7 ^ { 2 } + 4 ^ { 2 } }$

$= \sqrt { 100 + 49 + 16 } = \sqrt { 165 }$

Area of triangle