Question

If a = 6, −9, 3 , then what is 4a?

Answer 1

Answer:

Option 2.

Step-by-step explanation:

It is given that

a = <6,-9,3>

We need to compare the maginitude of vertor a and vector 4a.

If a vector is defined as v = <x,y,z>, then its magnitude is defined as

$|v|=\sqrt{x^2+y^2+z^2}$

Using the above formula we get

$|a|=\sqrt{6^2+(-9)^2+(3)^2}$

$|a|=\sqrt{126}$

$|a|=\sqrt{9\times 14}$

$|a|=3\sqrt{14}$

The vector 4a is  

$4a==$

$|4a|=\sqrt{(24)^2+(-36)^2+(12)^2}$

$|4a|=\sqrt{4^2(6^2+(-9)^2+(3)^2)}$

$|4a|=4\sqrt{6^2+(-9)^2+(3)^2}$

$|4a|=4|a|$

The magnitude of 4a is a factor of 4 greater than the magnitude of a.

Therefore, the correct option is 2.