Find the volume of tetrahedron (in cubic units) whose coterminus edges are $7^i +^k; 2^i + 5^j - 3^k$ and $4^i + 3^j +^k$

Open in App

Solution

We know that the volume of a tetrahedron with coterminus edges $a, b$ and $c$ is $\frac{1}{6} [\to a \to b \to c]$
Here, $\to a = 7^i +^k, \to b = 2^i + 5^j - 3^k$ and $4^i + 3^j +^k$
$[\to a \to b \to c] = \to a \cdot (\to b \times \to c)$
$= ∣ ∣ ∣ ∣ \begin{matrix} 7 & 0 & 1 2 & 5 & - 3 4 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣$
$= 7 (5 + 9) - 0 (2 + 12) + 1 (6 - 20)$
$= 98 - 0 - 14 = 84$
$∴$ Volume of tetrahedron $= \frac{1}{6} [\to a \to b \to c] = \frac{1}{6} \times 84 = 14$ cubic units.

Suggest Corrections

Similar questions

2^i + 3^j - 4^k, 5^j + 7^j + 5^k

4^i + 4^j - 2^k

- - \to O A = 2^i - 3^j + 0^k,

- - \to O B =^i +^j -^k

- - \to O C = 3^i - 3^k

a = 2^i - 6^j - 3^k, b = 4^i + 3^j -^k

4^i + 3^j +^k, 5^i + 9^j + 19^k

8 i + 6 j + 5 k

^i -^j +^k, 2^i - 4^j + 5^k,^3 i - 5^j + 2^k

Join BYJU'S Learning Program