Question

1: Give the short answer of following questions:
At what angle components of a vector have same magnitude? Explain
Find the unit vector in the direction of 4î+4j-2 k.
Find pair of forces which gives a resultant of 15N?
Explain head to tail rule for adding the vector.
Deline unit vector and null vector with examples.
Define position vector. How is it expressed in two and three dimensions?
Find the magnitude of unit vector as given A=4ſ+3j/5.
The vector sum of three vectors gives a zero resultant. What can be orientat
Find F. coniponent of a force vector Fof magnitude 30N making can angle
If Ax=Ay, then find the angle which the vector A makes with x-axis?
If a force of 100N makes an angle of 60° with x-axis, what will be its x-com
If the resultant of the two vectors of magnitude 5 and 1​

Answer 1

1) Components of a vector a can be broken down into -

a cosx and a sinx , where x is the angle


When x = 45
cos x = sin x = 1/root2


Therefore
The components can be written as -

a cosx = a/root2
a sinx = a/ root2

Hence, magnitude same for 45 degrees.



2) to find the unit vector we divide the vector by its magnitude


4i+4j-2k magnitude = root( 4^2 + 4^2 + (-2^2) )
=root(16+16+4)=root(36)=6

Ans - 4/6 i + 4/6 j - 2/6 k


3) one such example can be - 6i , 9i


4) while adding two or more vector, we first make another vector joining the tail of one vector to the head of the other vector. This is called head to tail rule.


5) Unit vector - Vectors of magnitude 1 ex- î , j , k
Null vector - vectors of magnitude 0


6) Position vector of the particles is the combination of the unit vectors along the axis X,Y,Z.

The position in X axis is expressed with unit vector i
“ “ Y “ “ “ j
“ Z “ “ K


7) All unit vectors have magnitude = 1



8)the orientation can be an equilateral triangle




9) - question unclear -




10) refer to answer 1
Ans - 45


11) x component = a cosx
100 cos 60 = 100/2 = 50 N


12) resultant magnitude - both magnitudes can simply be added

5 + 1 =6