OPERATIONS WITH VECTORS

  • Sum of two vectors will also be a vector.
  • Difference of two vector is also be a vector.
  • Multiplying a scalar by a vector will also produce vector.

Adding Vectors

Example :

Solution :

Subtracting Vectors

Example :

Solution :

Multiplying Scalar

Example :

Solution :

Problem 1 :

Find a+b where a=14 and b=25

Solution:

a+b=14+25=1+24+5a+b=39

Problem 2 :

Find c-d where c=42 and d=15

Solution:

c-d=42-15=4-12-5c-d=3-3

Problem 3 :

Find 3u where u=-27.

Solution:

u=-273u=3-273u=-621

Problem 4 :

Find 2a+b where a=-13 and b=46.

Solution:

2a+b=2-13+46=-26+46=-2+46+62a+b=212

Problem 5 :

Find u-2v where u=50 and v=2-3.

Solution:

u-2v=50-22-3=50-4-6=5-40+6u-2v=16

Problem 6 :

Find 4b+2c where b=34 and c=-15.

Solution:

4b+2c=434+2-15=1216+-210=12-216+104b+2c=1026

Problem 7 :

Find -2a+b where a=37 and b=6-2.

Solution:

-2a+b=-237+6-2=-6-14+6-2=-6+6-14-2-2a+b=0-16

Problem 8 :

Find a-2b where a=34 and b=13.

Solution:

a-2b=34-213=34-26=3-24-6a-2b=1-2

Problem 9 :

Find 4u-3v where u=45 and v=23.

Solution:

4u-3v=445-323=1620-69=16-620-94u-3v=1011

Problem 10 :

Find a+b+c where a=-23, b=45 and c=6-7.

Solution:

a+b+c=-23+45+6-7=-2+4+63+5-7=81

Problem 11 :

Find 2u+v-3w where u=43, v=0-1 and w=22.

Solution:

2u+v-3w=243+0-1-322=86+0-1-66=8+0-66-1-6=2-1

Problem 12 :

Find a+2b-3c where a=2522, b=23 and c=45.

Solution:

a+2b-3c=2522+223-345=2522+46-1215=25+4-1222+6-15=1713

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