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V E C T O R

IISY. IISY. V E C T O R. GRADE X. Sutarman. 2008. The Definition. A vector is a quantity with both magnitude and direction. terminal point. B. or a. We use symbol. to denote this vector. a. or | a |. We use symbol. to denote the magnitude of this vector. A. initial

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V E C T O R

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1. IISY IISY V E C T O R GRADE X Sutarman 2008

2. The Definition A vector is a quantity with both magnitude and direction. terminal point B or a We use symbol to denote this vector. a or |a| We use symbol to denote the magnitude of this vector. A initial point

3. Equal Vectors When vectors have the same direction and magnitude, they are said to be equal vectors. p q a b c In the figure above, a= b = c and p = q

4. Quiz • Which are the equal vectors? h f j c a g i k b d e l

5. Addition of Vectors • Using Triangle Law of Vector Addition a resultant vector a + b b b a

6. Quiz • Find the resultant vector of a + b + c. b c a c a b a+b+c

7. Null Vector • The triangle is given a translation afollowed by translation bso that the final position of the figure is the same as before. The result of these translations is equivalent to the null translation, we write a + b = 0. Here null vector or zero vector is denoted by 0. a b

8. Negative of a Vector In a + b = 0, • magnitude of bis equal to the magnitude of a • direction of b is opposite to that of a. a b bis negative of a We write b = -a.

9. Subtraction of Vectors • Note thatp – q = p + (-q) orp – q = -q + p -q p p-q p q

10. Quiz • Find the resultant vector of a- b. b a a-b a -b

11. Scalar Multiplication of Vectors 2a is a vector which has the same direction as a. The magnitude of 2a is twice that of a. Symbolically, we write |2a| = 2|a|. Multiplier 2 is referred to as a scalar. In general, multiplying a vector by a scalar k gives ka. k always non-negative. 2a a a

12. Scalar Multiplication of Vectors What happens if the scalar is -2 ? 2a -2a a

13. a - a a a Quiz Name each vectors below! -2a a -3a 2a 3a

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