Two vectors P and Q of magnitudes 5 and 3 units respectively are inclined at an angle of 30 to each other.calculate the component of the resultant in the direction of Q.

Make your sketch.

Method 1, complete the parallelogram and find the diagonal
x^2 = 5^2 + 3^2 - 2(5)(3)cos 150°
= 59.9807...
x = appr 7.74

(exact value: x^2 = 34 + 30√3/2
= 34 + 15√3
x = √(34 + 15√3) )

method 2
place vector P along the horizontal
so vector P = (5,0)
vector Q is (3cos30, 3sin30)
P+Q = (5,0) + (3√3/2, 3/2)
= ( 5+3√3/2 , 3/2)

maginitude = √( (5+3√3/2)^2 + 9/4 ) = appr 7.44
same as above

Yes

D resultant is 7.74

I don't understand

Two vectors a and B of magnitude of 5 and 3 Unit respectively are inclined at an angle of 30 degree to each other. Calculate the resultant of the two vectors

To calculate the component of the resultant vector in the direction of vector Q, we need to find the dot product of the resultant vector and vector Q.

Let's break down the problem step by step:

Step 1: Find the magnitude of the resultant vector (R):
To find the magnitude of the resultant vector, we need to use the law of cosines:
R^2 = P^2 + Q^2 - 2(P)(Q)cos(theta)
R^2 = 5^2 + 3^2 - 2(5)(3)cos(30)
R^2 = 25 + 9 - 30√(3)/2
R^2 = 34 - 15√(3)
R ≈ 5.63 (rounded to two decimal places)

Step 2: Find the angle between the resultant vector (R) and vector Q:
To find this angle, we can use the law of sines:
sin(theta) / Q = sin(90) / R
sin(theta) = Q * sin(90) / R
sin(theta) = 3 * 1 / 5.63
sin(theta) ≈ 0.53
theta ≈ arcsin(0.53)
theta ≈ 32.3 degrees (rounded to one decimal place)

Step 3: Find the component of the resultant vector in the direction of vector Q:
To calculate this component, we use the formula:
Component in Q direction = R * cos(theta)
Component in Q direction ≈ 5.63 * cos(32.3)
Component in Q direction ≈ 4.71 (rounded to two decimal places)

Therefore, the component of the resultant vector in the direction of vector Q is approximately 4.71 units.

Two vector P and Q of magnitude 5 and 3 unit respectively are inclined at an angle 30° to each other.calculate the resultant in the direction of Q and perpendicular to the direction of Q