Question

Find

(1) a + b,
(2) 2a + 3b,
(3) |a|, and |a − b|.
a = 5i + j, b = i − 2j

Answer 1

Explanation:

this problem is on vector

given the vectors

a = 5i + j, and

b = i − 2j

1. summation of vector a + b

`= (5i+j)+(i-2j)\\\\=5i+j+i-2j\\\\`

collect like terms

`=5i+i+j-2j\\\\=6i-j\\\\`

2. 2a + 3b

`= 2(5i+j)+3(i-2j)\\\\=10i+2j+3i-6j\\\\`

collecting like terms we have

`=10i+2j+3i-6j\\\\=10i+3i+2j-6j\\\\=13i-4j`

(3) |a|, and |a − b|.

|a|= |5i+j|

`=√(5^2+1^2) \\\\=√(25+1) \\\\=√(26) \\\\= 5.1`

also,

`|a - b|= |(5i+j) -(i-2j)| \\\\ a-b= 5i+j -i+2j \\\\ a-b=5i-i+j+2j \\\\a-b= 4i+3j\\\\`

`|a -b|=√(4^2+3^2) \\\\|a -b|=√(16+9) \\\\|a -b|=√(25) \\\\|a -b|=25`