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

question 135

Multiple Choice

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

• A) \(\mathbf { v } _ { 1 } = \frac { 7 } { 2 } \mathrm { i } + \frac { 7 } { 2 } \mathrm { j } , \mathrm { v } _ { 2 } = - \frac { 5 } { 2 } \mathrm { i } + \frac { 3 } { 2 } \mathrm { j }\)
• B) \(\left. \mathbf { v } _ { 1 } = 3 \mathbf { i } + 3 \mathbf { j } \right) , \mathbf { v } _ { 2 } = - 2 \mathbf { i } + 2 \mathbf { j }\)
• C) \(\mathbf { v } _ { 1 } = 6 \mathbf { i } + 6 \mathbf { j } , \mathbf { v } _ { 2 } = - 4 \mathbf { i } + 4 \mathbf { j }\)
• D) \(\mathbf { v } _ { 1 } = 3 \mathbf { i } + 3 \mathbf { j } , \mathbf { v } _ { 2 } = 2 \mathbf { i } - 2 \mathbf { j }\)

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