Decompose V into Two Vectors V1 and V2, Where V1 $$\mathbf { v } = - 3 \mathbf { i } - 5 \mathbf { j } , \quad \mathbf { w } = 2 \mathbf { i } - \mathbf { j }$$

question 237

Multiple Choice

Decompose v into two vectors v1 and v2, where v1 is parallel to w and v2 is orthogonal to w.
- $$\mathbf { v } = - 3 \mathbf { i } - 5 \mathbf { j } , \quad \mathbf { w } = 2 \mathbf { i } - \mathbf { j }$$

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

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