Three Vectors A, B, and C Are Given $\mathbf { a } \cdot ( \mathbf { b } \times \mathbf { c } )$

question 25

Short Answer

Three vectors a, b, and c are given.
(a) Find their scalar triple product
$\mathbf { a } \cdot ( \mathbf { b } \times \mathbf { c } )$ .
(b) Are the vectors coplanar? If not, find the volume of the parallelepiped that they determine.
$\mathbf { a } = \langle 3,0 , - 4 \rangle , \mathbf { b } = \langle 2,2,2 \rangle , \mathbf { c } = \langle 7,4,0 \rangle$

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Definitions:

Median

The middle value in a sorted list of numbers, effectively dividing the dataset into two equal parts.

75th Percentile

A value below which 75% of the observations in a group fall, often used to measure the upper quartile.

Coefficient Of Variation

A standardized measure of the dispersion of a probability distribution or frequency distribution, often used to compare the degree of variation between different datasets.

Ages

Quantitative measures representing lengths of time that entities, typically individuals, have existed from birth to a specific reference point.