Let $\vec { v } _ { 1 } = 2 \vec { i } - 4 \vec { j } + \vec { k }$

question 8

Essay

Let $\vec { v } _ { 1 } = 2 \vec { i } - 4 \vec { j } + \vec { k }$ and $\vec { v } _ { 2 } = 4 \vec { i } + \vec { j } + \vec { k }$ Find a vector which is perpendicular to $\vec { v } _ { 1 }$ and $\vec { v } _ { 2 }$ to find an equation of the plane through the point (1, 2, -1)and with normal vector perpendicular to both $\vec { v } _ { 1 }$ and $\vec { v } _ { 2 }$ .Express your answer in the form $A x + B y + C z = D$

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Definitions:

Pearson Correlation

A coefficient that measures the linear correlation between two variables X and Y, giving a value between -1 and 1.

Coefficient

A multiplicative factor in mathematical expressions, often used to describe the relationship between variables in statistical models.

Research Hypothesis

Statement regarding an expected or predicted relationship between variables.

Ordinal Variables

Variables that represent categories with a natural order or ranking, but where the distances between categories are not necessarily equal.