4.2 Multiplication of Vector by a Scalar and the Parallel Condition of Two Vectors

4.2 Multiplication of Vector by a Scalar and the Parallel Condition of Two Vectors
1. When a vector a ˜ is multiplied by a scalar k, the product is k a ˜ . Its magnitude is k times the magnitude of the vector a ˜ .

2. The vector a ˜ is parallel to the vector b ˜ if and only if b ˜ =k a ˜ , where k is a constant.

3. If the vectors a ˜ and b ˜ are not parallel and h a ˜ =k b ˜ , then h = 0 and k = 0.


Example 1:
If vectors a ˜  and  b ˜  are not parallel and ( k7 ) a ˜ =( 5+h ) b ˜ , find the value of k and of h.

Solution:
The vectors a ˜  and  b ˜ are not parallel, so
k – 7 = 0 → k = 7
5 + h = 0 → h = –5