Question

What is the area of triange formed by
$a = 2i - 3j + 4k$
and
$b = i - k$
and their resultant???

$(a) \: \sqrt{13.5} \\ \\ (b) \: 13.5 \\ \\ (c) \: \sqrt{38.7} \\ \\ (d) \: 38.7$
​

Answer 1

Area of triangle = $\large\rm { \frac {1}{2} | \vec {A} × \vec {B} | }$

$\large\rm { \frac {1}{2} × \left\Bigg|</p><p>\begin{array}{ c c c } </p><p>\hat{i} & \hat{j} & \hat{k} \\ </p><p>2 & -3 & 4 \\</p><p>1 & 0 & - 1 \\</p><p>\end{array}</p><p>\right\Bigg| }$

$\large\rm { = \frac {1}{2} | [ \hat{i} (3-0) - \hat{j} (-2-4) \hat{k}(+3)] | }$

$\large\rm { = \frac {1}{2} \sqrt {9+36+9} }$

so, second option , i.e. √13.5 is correct.

Answer 2

Answer:

Area of triangle = \large\rm { \frac {1}{2} | \vec {A} × \vec {B} | }

2

1

∣

A

×

B

∣

\begin{gathered}\large\rm { \frac {1}{2} × \Bigg| \begin{array}{ c c c } \hat{i} & \hat{j} & \hat{k} \\ 2 & -3 & 4 \\ 1 & 0 & - 1 \\ \end{array} \Bigg| }\end{gathered}

2

1

×

∣

∣

∣

∣

∣

∣

i

^

2

1

j

^

−3

0

k

^

4

−1

∣

∣

∣

∣

∣

∣

\large\rm { = \frac {1}{2} | [ \hat{i} (3-0) - \hat{j} (-2-4) \hat{k}(+3)] | }=

2

1

∣[

i

^

(3−0)−

j

^

(−2−4)

k

^

(+3)]∣

\large\rm { = \frac {1}{2} \sqrt {9+36+9} }=

2

1

9+36+9

so, second option , i.e. √13.5 is correct.