Question

Each of the following vectors is given in terms of its x and y components. Find the magnitude of each vector and the angle it makes with respect to the +x axis.

a- AxAx = -1, AyAy = -6. Find the magnitude of this vector. (Express your answer to two significant figures.)

b- AxAx = -1, AyAy = -6. Find the angle this vector makes with respect to the +x axis. Use value from -180∘∘ to +180 ∘∘. (Express your answer to two significant figures.)

c- AxAx = -6, AyAy = -2. Find the magnitude of this vector. (Express your answer to two significant figures.)

d- AxAx = -6, AyAy = -2. Find the angle this vector makes with respect to the +x axis. Use value from -180∘∘ to +180 ∘∘. (Express your answer to two significant figures.)e-

e- AxAx = -4, AyAy = -6. Find the magnitude of this vector. (Express your answer to two significant figures.)

f- AxAx = -4, AyAy = -6. Find the angle this vector makes with respect to the +x axis. Use value from -180∘∘ to +180 ∘∘. (Express your answer to two significant figures.)

Answer 1

a) X- component of vector = -1

Y- component of vector = - 6

Magnitude of the vector (,) is given by = , where a and b is the magnitude of vectors and

is the angle between vectors.

Here two vectors are perpendicular to each other so, .

So, magnitude = =    = 6.08

b) if we measure the angle made by vector in anti clockwise direction then it is positive and in clockwise direction negative.

If, we measure the angle in anti clockwise direction then it will be more than 180⁰ ( See fig.).

And range is given between 180⁰ and - 180⁰.  

From figure,

Angle made by the vector with positive x- axis = 90⁰+ 9.46⁰= 99.46⁰  

c)  

X- component of vector = -6

Y- component of vector = - 2

Magnitude of the vector (,) is given by = , where a and b is the magnitude of vectors and

is the angle between vectors.

Here two vectors are perpendicular to each other so, .

So, magnitude = =    = 6.32

d)  

if we measure the angle made by vector in anti clockwise direction then it is positive and in clockwise direction negative.

If, we measure the angle in anti clockwise direction then it will be more than 180⁰ ( See fig.).

And range is given between 180⁰ and - 180⁰.  

From figure,

Angle made by the vector with positive x- axis = 90⁰+ 71.56⁰= 161.56⁰  

e)

X- component of vector = -4

Y- component of vector = - 6

Magnitude of the vector (,) is given by = , where a and b is the magnitude of vectors and

is the angle between vectors.

Here two vectors are perpendicular to each other so, .

So, magnitude = =    = 7.21

f)

if we measure the angle made by vector in anti clockwise direction then it is positive and in clockwise direction negative.

If, we measure the angle in anti clockwise direction then it will be more than 180⁰ ( See fig.).

And range is given between 180⁰ and - 180⁰.  

From figure,

Angle made by the vector with positive x- axis = 90⁰+ 33.69⁰= 123.69⁰