Answer:
the resultant of the two vectors 5 km SW and 12 km NW is a vector pointing 67.4 degrees north of west with a length of 13 km.
Step-by-step explanation:
To find the resultant of two vectors, we need to draw them on a graph and then use vector addition. In this case, "SW" means "southwest" and "NW" means "northwest". We can represent "SW" as a vector pointing 45 degrees south of west (since southwest is halfway between south and west) and "NW" as a vector pointing 45 degrees north of west (since northwest is halfway between north and west).
We can then draw these two vectors on a graph with a scale of 1 cm = 1 km. The vector representing "5 km SW" will be 5 cm long and pointing 45 degrees south of west, and the vector representing "12 km NW" will be 12 cm long and pointing 45 degrees north of west.
To add these two vectors, we start by putting the tail of the second vector (12 km NW) at the head of the first vector (5 km SW). This creates a triangle with sides of 5 cm, 12 cm, and an unknown side representing the resultant vector. We can use the Pythagorean theorem to find the length of the resultant vector:
resultant^2 = 5^2 + 12^2
resultant^2 = 25 + 144
resultant^2 = 169
resultant = sqrt(169)
resultant = 13
So the length of the resultant vector is 13 cm, which represents 13 km. To find the direction of the resultant vector, we can use trigonometry. The angle between the first vector (5 km SW) and the resultant vector is equal to the angle whose tangent is 12/5 (the ratio of the opposite and adjacent sides of the triangle). We can use a calculator to find that this angle is approximately 67.4 degrees north of west.
Therefore, the resultant of the two vectors 5 km SW and 12 km NW is a vector pointing 67.4 degrees north of west with a length of 13 km.