Home
Class 12
PHYSICS
A vector lying in x-y plane has a magnit...

A vector lying in x-y plane has a magnitude 3, and makes an angle `30^(@)` with the x-axis. Find its components along the two axes.

Text Solution

Verified by Experts

Let the vector be `barA` .
Then `|barA| = 3 , theta , = 30^(@)`
`A_(x) = A cos theta`
`=3 cos 30^(@)`
`=3xx(sqrt(3))/(2)`
`=(3sqrt(3))/(2),`
`A_(y)= Asin theta`
`=3 sin 30^(@)`
`=(3)/(2)`
Thus the two rectangular components are `A_(x) = (3sqrt(2))/(2) ` and `A_(y) = (3)/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A vector of magnitude 13 makes an angle 65.37^(@) with the x-axis . What is its component along positive y-axis ?

A displacement vector of magnitude 4 makes an angle 30^(@) with the x-axis. Its rectangular components in x-y plane are

A displacment vector fo magnitude 4 makes an angle 30^(@) with the x-axis. Its rectangular components in x-y plane are

Let AB be a vector in two dimensional plane with the magnitude 4 units and making an angle of 30^(@) with X-axis and lying in the first quadrant. Find the components of AB along the two axes off coordinates. Hence, represent AB in terms of unit vectors hati and hatj .

A tangent to the parabola y^(2)=16x makes an angle of 60^(@) with the x-axis. Find its point of contact.

A rectangular loop consists of N = 100 closed wrapped turns and has dimensions (0.4 m xx 0.3 m) . The loop is hinged along the y-axis and its plane makes an angle theta = 30^@ with the x-axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field B = 0.8 T directed along the x-axis when current is i = 1.2 A in the direction shown. What is the expected direction of rotation of the loop?

A vector having magnitude 30 unit makes equal angles with each of X,Y, and Z -axes The components of vector along each of X,Y,and Z -axes are

X- component of vec(a) is twice of its Y- component. If the magnitude of the vector is 5sqrt(2) and it makes an angle of 135^(@) with z-axis then the components of vector is:

Let vec(AB) be a vector in two dimensional plane with magnitude 4 units. And making an anle of 60^0 with x-axis, and lying in first quadrant. Find the components of vec(AB) in terms of unit vectors hati and hatj . so verify that calculation of components is correct.

A vector vecA makes an angle of 20^@ and vecB makes an angle of vec110^@ with the X-axis. The magnitude of these vectors are 3 m and 4 m respectively.Find the resultant