The sum of two vectors of fixed magnitudes has its minimum magnitude when the angle between these vectors is

The minimum magnitude is obtained when two magnitude are summed when the angle between the vectors is 180°.

When the angle between the summed vectors is 0°, the cosine value obtained will be ; cos(0°) is 1.

Hence, the sum of the magnitude will use the addition operator.

When the angle between two summed vectors is 180°, the cosine value obtained ; cos(180°) is -1. Hence, the sum of the magnitudes will use the subtraction operator due to the negative sign.

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  180°

Step-by-step explanation:

When the angle between the vectors is 0°, the magnitudes add, so the sum will be a maximum. When the angle between the vectors is 180°, the resultant has a magnitude equal to the difference of the vector magnitudes. For angles between those extremes, the sum will be somewhere between those extremes.

The sum is a minimum when the angle between the vectors is 180°.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.