calculate Sia₁3D------12Calcule51) (a1a₂) (a3 a4) R:2) a1 (a2 + a3) R:3) a₂ a₁ + az ₁ R:36-236

The given vectors are: a1→=155 , a2→=312 , a3→=36-2 , a4→=-236 The dot product of two vectors…

Answered: a₁ = Calcule 5 5 " 3 d₂ = 1 1) (a1a₂)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

calculate

Si
a₁
3
D------
1
2
Calcule
5
1) (a1a₂) (a3 a4) R:
2) a1 (a2 + a3) R:
3) a₂ a₁ + az ₁ R:
3
6
-2
3
6

Expert Solution

Step 1

The given vectors are:

$\vec{a_{1}} = [\begin{matrix} 1 \\ 5 \\ 5 \end{matrix}], \vec{a_{2}} = [\begin{matrix} 3 \\ 1 \\ 2 \end{matrix}], \vec{a_{3}} = [\begin{matrix} 3 \\ 6 \\ - 2 \end{matrix}], \vec{a_{4}} = [\begin{matrix} - 2 \\ 3 \\ 6 \end{matrix}]$

The dot product of two vectors $\vec{x} = [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}]$ and $\vec{y} = [\begin{matrix} y_{1} \\ y_{2} \\ y_{3} \end{matrix}]$ is defined as $x \cdot y = (x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3})$ .