Question

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

Answer 1

Answer:

Step-by-step 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|

$=\sqrt{5^2+1^2} \\\\=\sqrt{25+1} \\\\=\sqrt{26} \\\\= 5.1$

also,

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

$|a -b|=\sqrt{4^2+3^2} \\\\|a -b|=\sqrt{16+9} \\\\|a -b|=\sqrt{25} \\\\|a -b|=25$