The volume of parallelopipped formed by following 3 vectors will be___cubic units.

$\to a = 3^i - 2^j + 5^k \to b = 2^i + 2^j -^k \to c = - 4^i + 3^j + 2^k$

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Solution

As discussed in the hint the volume of parallelopipped spanned by the given 3 vectors is given by their scalar triple product.

So that is exactly what we will calculate.

$S o [\to a, \to b, \to c] = \to a . (\to b \times \to c) = ∣ ∣ ∣ ∣ \begin{matrix} 3 & - 2 & 5 2 & 2 & - 1 - 4 & 3 & 2 \end{matrix} ∣ ∣ ∣ ∣$

The first row contains the first vector, the second row contains the second vector and the third row contains the third vector. So above determinant will be equal to

$3 ((2 \times 2) - (3 \times - 1)) + 2 ((2 \times 2) - (- 1 \times - 4)) + 5 ((2 \times 3) - (2 \times 4))$ = 21 + 70 =91 cubic units

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Similar questions

The volume of parallelopipped formed by following 3 vectors will be___cubic units.

$\to a = 3^i - 2^j + 5^k \to b = 2^i + 2^j -^k \to c = - 4^i + 3^j + 2^k$

The volume of parallelopipped formed by following 3 vectors will be $- --- -$ cubic units.

$\to a = 3^i - 2^j + 5^k \to b = 2^i + 2^j -^k \to c = - 4^i + 3^j + 2^k$

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

\to c = 3^i +^j + 2^k

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

5^i + 2^j - 3^k

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

4^i + 4^j - 2^k

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