Question

$.$ Assume that $v_{1}, v_{2},$ and $v_{3}$ are vectors in $R^{3}$ that have their initial points at the origin. In each part, determine whether the three vectors lie on the same line. (a) $v_{1}=(-1,2,3), v_{2}=(2,-4,-6), v_{3}=(-3,6,0)$ (b) $\mathrm{v}_{1}=(2,-1,4), \mathrm{v}_{2}=(4,2,3), \mathrm{v}_{3}=(2,7,-6)$ (c) $\mathbf{v}_{1}=(4,6,8), \mathbf{v}_{2}=(2,3,4), \mathbf{v}_{3}=(-2,-3,-4)$

          $.$ Assume that $v_{1}, v_{2},$ and $v_{3}$ are vectors in $R^{3}$ that have their initial points at the origin. In each part, determine whether the three vectors lie on the same line.
(a) $v_{1}=(-1,2,3), v_{2}=(2,-4,-6), v_{3}=(-3,6,0)$
(b) $\mathrm{v}_{1}=(2,-1,4), \mathrm{v}_{2}=(4,2,3), \mathrm{v}_{3}=(2,7,-6)$
(c) $\mathbf{v}_{1}=(4,6,8), \mathbf{v}_{2}=(2,3,4), \mathbf{v}_{3}=(-2,-3,-4)$

Added by Kiara S.

Linear Algebra and Its Applications

David C. Lay, Steven R. Lay, Judi J.… 5th Edition

Instant Answer

Solved by Expert David Mccaslin

07/22/2022

Step 1

Step 1: Calculate $ v_2 \times v_3 $ for part (a): \[ v_2 \times v_3 = \begin{vmatrix} i & j & k \\ 2 & -4 & 6 \\ -3 & 6 & 0 \end{vmatrix} = 36i - 18j + 0k \] Show more…

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$.$ Assume that $v_{1}, v_{2},$ and $v_{3}$ are vectors in $R^{3}$ that have their initial points at the origin. In each part, determine whether the three vectors lie on the same line. (a) $v_{1}=(-1,2,3), v_{2}=(2,-4,-6), v_{3}=(-3,6,0)$ (b) $\mathrm{v}_{1}=(2,-1,4), \mathrm{v}_{2}=(4,2,3), \mathrm{v}_{3}=(2,7,-6)$ (c) $\mathbf{v}_{1}=(4,6,8), \mathbf{v}_{2}=(2,3,4), \mathbf{v}_{3}=(-2,-3,-4)$