Question

Two sides of a triangle are given by i+j+k and -i+2j+3k then area of triangle is?

Answer 1

Answer:

the formula is 1/2(A*B)

Explanation:

when i find vector product of a and b i get.

i-4j+3k.

=root(1+16+9)

=root(26).

area of triangle is 1/2of root (26)

Answer 2

The area of the triangle is $\frac{\sqrt{26}}{2}$ units

Step-by-step explanation:

Given: vectors $i+j+k$ and $-1+2j+3k$ which are the sides of a triangle

How to find the area of a triangle with sides in vector form?

Let a and b be two sides of a triangle

Area A is calculated by:

$A = \frac{1}{2} |a$ x $b|$

How to find cross-product?

axb= $\\| \left[\begin{array}{ccc}i&j&k\\a1&a2&a3\\b1&b2&b3\end{array}\right] |$

where, $a = a1i+ a2j+ a3k$

and $b = b1i+b2j+b3k$

Substituting the values of a and b we get:

($i+j+k$) x( $-1+2j+3k$) = $|\left[\begin{array}{ccc}i&j&k\\1&1&1\\-1&2&3\end{array}\right]|$

                                         =  $i-4j+3k$

To find area, we need to find the magnitude of axb:

|axb|  $= |i-4j+3k|$

        $= \sqrt{1^{2}+(-4)^{2}+3^{2} }$

        $=\sqrt{26}$

Hence, the area of triangle is $\frac{\sqrt{26}}{2}$ units.