Explanation Given: v = 〈 − 2 , 5 〉 w = 〈 3 , − 2 〉 Key concepts applied: Unit vector A unit vector simply denotes the direction. To find a unit vector with the same direction as a given vector, we divide by the magnitude of the vector. Vector operations Vector addition To add the vectors 〈 x 1 , y 1 〉 and 〈 x 2 , y 2 〉 , we add the corresponding components from each vector: 〈 x 1 + x 2 , y 1 + y 2 〉 . Scalar multiplication When we multiply a vector by a scalar, the result is a vector. When a vector is multiplied by a scalar i.e. a regular number, we multiply it on every component in the vector to get the resultant vector. The objective is to express i as a linear combination of the given vectors. Let r be the scalar multiplier of the vector v and let s be the scalar multiplier of the vector w . We know, i is the unit vector along the x -direction. Thus, the linear combination can be written as i = r v + s w . Calculations: By equating individual components independently, we can create a system of equations with which we can solve the scalar multipliers. i = r v + s w This can be rewritten as 〈 1 , 0 〉 = r 〈 − 2 , 5 〉 + s 〈 3 , − 2 〉 By equating individual components of the vectors, we get the following system of equations, − 2 r + 3 s = 1 → ( 1 ) 5 r − 2 s = 0 → ( 2 ) Description − 2 r + 3 s = 1 → ( 1 ) 5 r − 2 s = 0 → ( 2 ) Step 1...

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Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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An expression for the unit vector i as a linear combination of the given vectors .

Solution Summary: The author explains how the unit vector i is expressed as a linear combination of the given vectors.

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An expression for the unit vector $i$ as a linear combination of the given vectors.

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Chapter 13 Solutions

An expression for the unit vector i as a linear combination of the given vectors .

Solution Summary: The author explains how the unit vector i is expressed as a linear combination of the given vectors.

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An expression for the unit vector i as a linear combination of the given vectors.

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Chapter 13 Solutions

An expression for the unit vector $i$ as a linear combination of the given vectors.