Find the length of each vector below. a. a= 2x+ 3y
b. a=x+y
c. a= 2x– 3y
d. a=x– 6y

a. 3.6 units

b. 1.4 units

c. 3.6 units

d. 6.1 units

Explanation:

The length of a vector is given by the following formula:

Length = √(x² + y²)

where,

x = x-component of vector

y = y-component of vector

a.

Here,

x = 2

y = 3

Therefore,

Length = √(2² + 3²)

Length = √13

Length = 3.6 units

b.

Here,

x = 1

y = 1

Therefore,

Length = √(1² + 1²)

Length = √2

Length = 1.4 units

c.

Here,

x = 2

y = -3

Therefore,

Length = √(2² + (-3)²)

Length = √13

Length = 3.6 units

d.

Here,

x = 1

y = -6

Therefore,

Length = √(1² + (-6)²)

Length = √37

Length = 6.1 units

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