SATHEE: Vectors 3 Question 16

Vectors 3 Question 16

16. The volume of the parallelopiped whose sides are given by $\vec{O A} = 2 \hat{i} - 3 \hat{j}, \vec{O B} = \hat{i} + \hat{j} - \hat{k}$ ,

$\vec{O C} = 3 \hat{i} - \hat{k}$ , is

(1983, 1M)

(a) $\frac{4}{13}$

(b) 4

(c) $\frac{2}{7}$

(d) None of these

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Answer:

Correct Answer: 16. (b)

Solution:

The volume of parallelopiped $= [\vec{a} \vec{b} \vec{c}] = | \begin{array}{ccc} 2 & - 3 & 0 1 & 1 & - 1 3 & 0 & - 1 \end{array} |$

$= 2 (- 1) + 3 (- 1 + 3) = - 2 + 6 = 4$

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Vectors 3 Question 16

16. The volume of the parallelopiped whose sides are given by OA→=2i^−3j^,OB→=i^+j^−k^,

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16. The volume of the parallelopiped whose sides are given by $\vec{O A} = 2 \hat{i} - 3 \hat{j}, \vec{O B} = \hat{i} + \hat{j} - \hat{k}$ ,