The volume (in cubic units) of the tetrahedron with edges hat i + widehat j + hat k , hat i - hat j + hat k and hat i +2 hat j - hat k is

Question

The volume (in cubic units) of the tetrahedron with edges hat i + widehat j + hat k , hat i - hat j + hat k and hat i +2 hat j - hat k is (A) 4 (B) 2 / 3 (C) 1 / 6 (D) 1 / 3

Tardigrade Admin · Accepted Answer

We know that, volume of tetrahedron =(1/6)[ A B A C A D ] =(1/6)| 1 1 1 1 -1 1 1 2 -1 | =(1/6)[1(1-2)-1(-1-1)+1(2+1)] =(1/6)[-1+2+3] =(4/6)=(2/3)

Q. The volume (in cubic units) of the tetrahedron with edges $\hat{i} + j + \hat{k}, \hat{i} - \hat{j} + \hat{k}$ and $\hat{i} + 2 \hat{j} - \hat{k}$ is

4

2 / 3

1 / 6

1 / 3

We know that, volume of tetrahedron
$= \frac{1}{6} [A B A C A D]$
$= \frac{1}{6} ∣ ∣ 111 1 - 1 2 11 - 1 ∣ ∣$
$= \frac{1}{6} [1 (1 - 2) - 1 (- 1 - 1) + 1 (2 + 1)]$
$= \frac{1}{6} [- 1 + 2 + 3]$
$= \frac{4}{6} = \frac{2}{3}$

Q. The volume (in cubic units) of the tetrahedron with edges i^+j​+k^,i^−j^​+k^ and i^+2j^​−k^ is

4

2 / 3

1 / 6

1 / 3

We know that, volume of tetrahedron =61​[ABACAD] =61​∣∣​111​1−12​11−1​∣∣​ =61​[1(1−2)−1(−1−1)+1(2+1)] =61​[−1+2+3] =64​=32​

Q. The volume (in cubic units) of the tetrahedron with edges $\hat{i} + j + \hat{k}, \hat{i} - \hat{j} + \hat{k}$ and $\hat{i} + 2 \hat{j} - \hat{k}$ is

We know that, volume of tetrahedron
$= \frac{1}{6} [A B A C A D]$
$= \frac{1}{6} ∣ ∣ 111 1 - 1 2 11 - 1 ∣ ∣$
$= \frac{1}{6} [1 (1 - 2) - 1 (- 1 - 1) + 1 (2 + 1)]$
$= \frac{1}{6} [- 1 + 2 + 3]$
$= \frac{4}{6} = \frac{2}{3}$