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

question 46

Multiple Choice

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

• A) \(\mathbf { v } _ { 1 } = - \frac { 12 } { 5 } \mathbf { i } - \frac { 4 } { 5 } \mathrm { j } , \mathbf { v } _ { 2 } = - \frac { 6 } { 5 } \mathrm { i } - \frac { 21 } { 10 } \mathrm { j }\)
• B) \(\mathbf { v } _ { 1 } = - \frac { 8 } { 3 } \mathbf { i } - \frac { 8 } { 9 } \mathbf { j } , \mathbf { v } _ { 2 } = \frac { 2 } { 3 } \mathbf { i } - \frac { 10 } { 9 } \mathrm { j }\)
• C) \(\mathbf { v } _ { 1 } = - \frac { 12 } { 5 } \mathbf { i } - \frac { 4 } { 5 } \mathbf { j } , \mathbf { v } _ { 2 } = - \frac { 4 } { 5 } \mathbf { i } - \frac { 8 } { 5 } \mathbf { j }\)
• D) \(\mathbf { v } _ { 1 } = - \frac { 12 } { 5 } \mathbf { i } - \frac { 4 } { 5 } \mathbf { j } , \mathbf { v } _ { 2 } = \frac { 2 } { 5 } \mathbf { i } - \frac { 6 } { 5 } \mathbf { j }\)

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