 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that a vector w has magnitude 130 and is inclined 40 degrees with horizontal. Result the vector into horizontal and vertical components. Horizontal component is given by magnitude of w into cos of theta and vertical component is given by magnitude of w into sin of theta where theta is the angle made by the vector w with horizontal. With this key idea let us proceed to the solution. So first we shall draw the figure showing horizontal and vertical vectors u and v respectively whose sum is w. Now this is vector u, this is vector v and their resultant u plus v is given by vector w. Here horizontal component is magnitude of u and vertical component is magnitude of v and we are given magnitude of w which is equal to 130 and theta which is equal to 40 degrees. Now using the key idea we will find horizontal and vertical components and we know that horizontal component is given by magnitude of w into cos theta and vertical component is given by magnitude of w into sin theta where theta is the angle made by the vector w with horizontal. So we have horizontal component that is magnitude of u which is equal to magnitude of w into cos of theta. Now we put the values of magnitude of w and theta in this equation and we get magnitude of u is equal to 130 into cos of angle 40 degrees which is equal to 130 into, now cos of 40 degrees is equal to 0.766. Now we have 130 into 0.766 which is approximately equal to 99.6. So horizontal component that is magnitude of u is approximately equal to 99.6. Similarly vertical component that is equal to magnitude of v is equal to magnitude of w into sin of theta which implies that magnitude of v is equal to magnitude of w that is 130 into sin of theta that is sin of 40 degrees which implies that magnitude of v is equal to 130 into, now sin of 40 degrees is equal to 0.642, 130 into 0.642 is approximately equal to 83. Thus horizontal component of w is 99.62 right and vertical component is 83 up which is the required answer. This completes our session. Hope you enjoyed this session.