Given two vectors a = 3.4i -3.9j and b =6.7i+8.3j what is the magnitude (in m) o

Question

Given two vectors a = 3.4i -3.9j and b =6.7i+8.3j

what is the magnitude (in m) of the vector a?

Find the direction (in ° = deg) of the vector a.

Find the direction (in °) of the vector b.

Find the direction of the vector a+b.

Find the direction (in ° = deg) of the vector a.

Find the magnitude of the vector b.

Find the direction (in °) of the vector b.

Find the magnitude of the vector a+b.

Find the direction of the vector a+b.

Find the magnitude of the vector a-b.

Find the direction of the vector a-b

Explanation / Answer

Here ,

a = 3.4 i - 3.9 j

b = 6.7 i + 8.3 j

a) magnitude of a = sqrt(3.4^2 + 3.9^2)

magnitude of a = 5.174 m

b) direction of vector a = arctan(-3.9/3.4)

direction of vector a = -48.9 degree

c) direction of vector b = arctan(8.3/6.7)

direction of vector b = 51.1 degree

d) for vector a + b

a + b = 3.4 i - 3.9 j + 6.7 i + 8.3 j

a + b = 10.1 i + 4.4 j

direction of a + b = arctan(4.4/10.1)

direction of a + b = 23.54 degree

e) direction of vector a = arctan(-3.9/3.4)

direction of vector a = -48.9 degree

f) magnitude of b = sqrt(6.7^2 + 8.3^2)

magnitude of b = 10.7 m

g) a + b = 10.1 i + 4.4 j

magnitude of a + b = sqrt(10.1^2 + 4.4^2)

magnitude of a + b = 11.1 m

i)

for vector a + b

a + b = 3.4 i - 3.9 j + 6.7 i + 8.3 j

a + b = 10.1 i + 4.4 j

direction of a + b = arctan(4.4/10.1)

direction of a + b = 23.54 degree

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