NIMCET 2016 — Mathematics PYQ

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Question

NIMCET 2016 — Mathematics PYQ

NIMCET | Mathematics | 2016

The volume of the parallelepiped determined by $u = i + 2 j - k, v = - 2 i + 3 k$ and $w = 7 j - 4 k$ is

Choose the correct answer:

Explanation

Concept:

The volume of the parallelepiped determined by $a$ , $b$ and $c$ is

Volume $= a \cdot (b \times c) =< / s p an >< s p an s t y l e = " f o n t - s i z e : 14 pt; " > a_{1} b_{1} c_{1} am p; a_{2} am p; b_{2} am p; c_{2} am p; a_{3} am p; b_{3} am p; c_{3}$

Calculation:

Parallelepiped determined by:
$u = \hat{i} + 2 \hat{j} - \hat{k}$
$v = - 2 \hat{i} + 3 \hat{k}$
$w = 7 \hat{j} - 4 \hat{k}$

$Volume = 1 - 2 0 am p; 2 am p; 0 am p; 7 am p; - 1 am p; 3 am p; - 4$

$\Rightarrow Volume = ∣1 (0 - 21) - 2 (8 - 0) + (- 1) (- 14 - 0) ∣$

$\Rightarrow Volume = ∣ - 23∣ = 23 units$