Home > Physics > Vector Operations

What is #|| <7, 3, -1> - < -2 , 5, 3 > ||#?

Answer 1

Leo Abeyta

#|| < 7,3,-1 > - < -2,5,3 >|| =sqrt(101)#.

See below.

To subtract two vectors #veca# and #vecb#:

#veca-vecb=< a_1-b_1,a_2-b_2, a_3-b_3 >#

The result is a vector, #vecc#.

The resulting vector's magnitude is then determined by:

#|vecc|=sqrt((c_1)^2+(c_2)^2+(c_3)^2)#

Given #veca=< 7,3,-1 ># and #vecb=< -2,5,3 >#,

#veca-vecb= < 7-(-2), 3-5, -1-3 >#

#=< 9, -2, -4 >#

Then, the magnitude is:

#|vecc|=sqrt(9^2+(-2)^2+(-4)^2)#

#=sqrt(101)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Benjamin Asiedu

To find the magnitude of the vector difference, subtract corresponding components and then find the magnitude of the resulting vector. The vector difference is: <7 - (-2), 3 - 5, -1 - 3> = <9, -2, -4>. The magnitude of the resulting vector is sqrt(9^2 + (-2)^2 + (-4)^2) = sqrt(81 + 4 + 16) = sqrt(101) ≈ 10.05.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

What is #|| &lt;7, 3, -1&gt; - &lt; -2 , 5, 3 &gt; ||#?

What is #|| <7, 3, -1> - < -2 , 5, 3 > ||#?