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Unformatted text preview: (Section 6.3: Vectors in the Plane) 6.18 SECTION 6.3: VECTORS IN THE PLANE Assume a , b , c , and d are real numbers. PART A: INTRO A scalar has magnitude but not direction. We think of real numbers as scalars, even if they are negative. For example, a speed such as 55 mph is a scalar quantity. A vector has both magnitude and direction. A vector v (written as v of v if you cant write in boldface) has magnitude v . The length of a vector indicates its magnitude. For example, the directed line segment (arrow) below is a velocity vector: An equal vector (together with labeled parts) is shown below. Vectors with the same magnitude and direction (but not necessarily the same position) are equal. PART B: SCALAR MULTIPLICATION OF VECTORS A scalar multiple of v is given by c v , where c is some real scalar. This new vector, c v , is c times as long as v . If c &lt; , then c v points in the opposite direction from the direction v points in. Examples: The vector 1 2 v is referred to as the opposite of 1 2 v . (Section 6.3: Vectors in the Plane) 6.19 PART C: VECTOR ADDITION Vector addition can correspond to combined (or net) effects. For example, if v and w are force vectors, the resultant vector v + w represents net force. Vector subtraction may be defined as follows: v- w = v +- w ( ) . There are two easy ways we can graphically represent vector addition: Triangle Law To draw v + w , we place the tail of w at the head of v , and we draw an...
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