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

question 214

Multiple Choice

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

• A) \(\mathbf { v } _ { 1 } = - \frac { 3 } { 10 } ( 3 \mathbf { i } + \mathbf { j } ) , \mathbf { v } _ { 2 } = - \frac { 11 } { 10 } \mathbf { i } + \frac { 33 } { 10 } \mathbf { j }\)
• B) \(\mathbf { v } _ { 1 } = - \frac { 3 } { 10 } ( 3 i + \mathbf { j } ) , \mathbf { v } _ { 2 } = - \frac { 17 } { 10 } \mathbf { i } + \frac { 12 } { 5 } \mathbf { j }\)
• C) \(\mathbf { v } _ { 1 } = - \frac { 1 } { 3 } ( 3 i + j ) , v _ { 2 } = - 1 i + \frac { 10 } { 3 } j\)
• D) \(\mathbf { v } _ { 1 } = - \frac { 3 } { 10 } ( 3 i + j ) , v _ { 2 } = \frac { 7 } { 10 } \mathbf { i } + \frac { 39 } { 10 } \mathbf { j }\)

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