6. A force \(\mathbf { F }\) is given by \(\mathbf { F } = ( 10 \mathbf { i } + \mathbf { j } ) \mathrm { N }\).
- Find the exact value of the magnitude of \(\mathbf { F }\).
- Find, in degrees, the size of the angle between the direction of \(\mathbf { F }\) and the direction of the vector \(( \mathbf { i } + \mathbf { j } )\).
The resultant of the force \(\mathbf { F }\) and the force \(( - 15 \mathbf { i } + a \mathbf { j } ) \mathrm { N }\), where \(a\) is a constant, is parallel to, but in the opposite direction to, the vector \(( 2 \mathbf { i } - 3 \mathbf { j } )\).
- Find the value of \(a\).
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