Solving for FBa: Why 59N and Not 50.6j + 8.43k?

[goldfish9776]

Homework Statement

why would we get 59N for FBa ? Isn't it equal to 50.6j +8.43k ?
they are j and k respectively , how could they sum up together? since dot product of j dot j is j , k dot k is k

Homework Equations

The Attempt at a Solution

 

[rozma3]

I believe it is the fact that when you use the dot product with two vectors, you end up with a scalar value or along that principle but not entirely certain. The calculation a.b = mag a x mag b x cos ab, so no vectors involved.

 

[QuantumQuest]

What is the dot product of j.j ? You have to understand why, for each such unit vector, this dot product is 1. As a hint, take the definition of dot product.

 

[goldfish9776]

What is the dot product of j.j ? You have to understand why, for each such unit vector, this dot product is 1. As a hint, take the definition of dot product.

as j dot j = 1 , so the product of j and j is only the scalar magnitude, with no unit ?

 

[faradayscat]

as j dot j = 1 , so the product of j and j is only the scalar magnitude, with no unit ?

$i,j,k$ are all vectors, to be more precise they are orthonormal vectors, this means they are all perpendicular to each other and their magnitude is 1. It's useful to use combinations of these vectors to find any vector $v$ in R3 (3D).

e.g.: $v = ai + bj + ck$

Where a,b,c are real numbers.

These vectors form an orthonormal basis in R3, but that's just a fancy term to say that these vectors can be combined to find ANY vector in 3D.

So, when you ask why $j•j$ has no unit, it makes no sense. The dot product gives a scalar;

$j•j = 1$

Since the magnitude of $j$ is 1.

 

[SammyS]

as j dot j = 1 , so the product of j and j is only the scalar magnitude, with no unit ?

The short answer is, Yes?

I assume you mean, no unit vector.