State Whether the Vectors Are Parallel, Orthogonal, or Neither $$\mathbf { v } = - 3 \mathbf { i } - 5 \mathbf { j } , \quad \mathbf { w } = 2 \mathbf { i } - \mathbf { j }$$

question 99

Multiple Choice

State whether the vectors are parallel, orthogonal, or neither.
- $$\mathbf { v } = - 3 \mathbf { i } - 5 \mathbf { j } , \quad \mathbf { w } = 2 \mathbf { i } - \mathbf { j }$$

• A) \(\mathbf { v } _ { 1 } = - \frac { 2 } { 5 } \mathbf { i } - \frac { 1 } { 5 } \mathbf { j } , \mathbf { v } _ { 2 } = \frac { 7 } { 5 } \mathbf { i } - \frac { 14 } { 5 } \mathrm { j }\)
• B) \(\mathbf { v } _ { 1 } = - \frac { 2 } { 5 } \mathrm { i } - \frac { 1 } { 5 } \mathrm { j } , \mathbf { v } _ { 2 } = - \frac { 14 } { 5 } \mathrm { i } - \frac { 24 } { 5 } \mathrm { j }\)
• C) \(\mathbf { v } _ { 1 } = - \frac { 1 } { 2 } \mathrm { i } - \frac { 1 } { 4 } \mathrm { j } , \mathbf { v } _ { 2 } = - \frac { 5 } { 2 } \mathrm { i } - \frac { 19 } { 4 } \mathrm { j }\)
• D) \(\mathbf { v } _ { 1 } = - \frac { 2 } { 5 } \mathrm { i } - \frac { 1 } { 5 } \mathrm { j } , \mathrm { v } _ { 2 } = - \frac { 13 } { 5 } \mathrm { i } - \frac { 24 } { 5 } \mathrm { j }\)

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Definitions:

Aldoses

A subclass of monosaccharides that contain an aldehyde group and multiple hydroxyl groups, responsible for various roles in living organisms.

Fructose

A simple ketonic monosaccharide found in many plants, sweeter than glucose, and used in foods and beverages.

Cyclic Hemiacetal

A molecule that results from the intramolecular reaction between an aldehyde and an alcohol in the same molecule, forming a cyclic structure with an ether bridge and an alcohol group.

Lactone

A cyclic ester that is formed by the intramolecular condensation of a hydroxy acid.