 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that write the given vector in component form. Now we know that every vector has two components horizontal component and vertical component. Also a vector is represented as the ordered pair xy which is the component form of the vector. When direction of a vector v is given as theta and magnitude is modulus of vector v then horizontal component x is equal to magnitude of v into cos of theta and vertical component is equal to y that is equal to magnitude of v into sin of angle theta. Thus component form of vector v is given by the ordered pair magnitude of v cos theta magnitude of v sin theta. With this key idea let us proceed to the solution. Now we are given a vector v whose direction angle is 60 degrees and magnitude is 5. Thus we have magnitude of v is equal to 5 and theta is equal to 60 degrees and we have to write this vector in component form. Using the key idea we will find its components and the horizontal component x is given by magnitude of v into cos of theta and vertical component y is given by magnitude of v into sin of theta where direction of a vector v is theta and magnitude is modulus of v. So horizontal component that is x is equal to magnitude of v into cos of theta. Now we put the values of magnitude of v and theta. So this implies that x is equal to 5 into cos of 60 degrees which further implies that x is equal to 5 into now cos of 60 degrees is equal to 1 by 2. So we have x is equal to 5 by 2. Now we shall find vertical component y which is given by y is equal to magnitude of v into sin of angle theta. Now again putting the values of magnitude of v and theta in this equation we get y is equal to 5 into sin of 60 degrees which further implies that y is equal to 5 into now sin of 60 degrees is equal to square root of 3 by 2 which implies that y is equal to 5 into square root of 3 by 2. So we get the value of x as 5 by 2 and the value of y as 5 into square root of 3 by 2. Thus the component form of the vector is given by the ordered pair magnitude of v cos of theta magnitude of v sin of theta and that is equal to the ordered pair 5 by 2 5 into square root of 3 by 2. Thus the component form of the given vector is the ordered pair 5 by 2 5 into square root of 3 by 2. This completes our session. Hope you enjoyed this session.