Chapter 9: Q. 56 (page 628)

Find the volume of a parallelepiped whose defining vectors are
$\vec{A} = <1, 0, 6> \vec{B} = <2, 3, - 8> \vec{C} = <8, - 5, 6>$

Short Answer

Expert verified

The volume is : 226 cubic units

Step by step solution

Step 1. given vectors

$\vec{A} = <1, 0, 6> \vec{B} = <2, 3, - 8> \vec{C} = <8, - 5, 6>$

Which can be written as :

$\vec{A} = \hat{i} + 0 \hat{j} + 6 \hat{k} \vec{B} = 2 \hat{i} + 3 \hat{j} - \hat{k} \vec{C} = 8 \hat{i} - 5 \hat{j} + 6 \hat{k}$

Step 2. Volume of parallelopiped

As given in question volume of parallelopiped is given by :

$V = |(A \times B) . C|$

So , Using this

$\vec{A} = \hat{i} + 0 \hat{j} + 6 \hat{k} \vec{B} = 2 \hat{i} + 3 \hat{j} - 8 \hat{k} \vec{C} = 8 \hat{i} - 5 \hat{j} + 6 \hat{k} V = |(A \times B) . C| V = | ((\hat{i} + 0 \hat{j} + 6 \hat{k}) \times (2 \hat{i} + 3 \hat{j} - 8 \hat{k})) . (8 \hat{i} - 5 \hat{j} + 6 \hat{k}) | V = | (- 18 \hat{i} + 20 \hat{j} + 3 \hat{k}) \times (8 \hat{i} - 5 \hat{j} + 6 \hat{k}) | V = | - 144 - 100 + 18 | V = 226 c u b i c u n i t s$

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Find the volume of a parallelepiped whose defining vectors are
$\vec{A} = <1, 0, 6> \vec{B} = <2, 3, - 8> \vec{C} = <8, - 5, 6>$

Short Answer

Step by step solution

Step 1. given vectors

Step 2. Volume of parallelopiped

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Find the volume of a parallelepiped whose defining vectors areA→=1,0,6B→=2,3,-8C→=8,-5,6

Short Answer

Step by step solution

Step 1. given vectors

Step 2. Volume of parallelopiped

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Find the volume of a parallelepiped whose defining vectors are
$\vec{A} = <1, 0, 6> \vec{B} = <2, 3, - 8> \vec{C} = <8, - 5, 6>$