What Is the Result of -4.00 C·(4.00 A×B) in Vector Calculations?

[Gattz]

Homework Statement

For the following three vectors, what is -4.00 C·(4.00 A×B)?
http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c03/eq03_86.gif"

Homework Equations

a x b = (a2b3 - a3b2) i + (a3b1 - a1b3) j + (a1b2 - a2b1) k

The Attempt at a Solution

I've multiplied 4 to each of the numbers in A, then plugged in numbers of A and B to the equation, next I multiplied -4 x C and used those to multiply the answer of A and B to get 224 + 1024 + 68k. I really am lost here.

Homework Statement

Use the definition of scalar product, vectors a ·b = ab cos θ, and the fact that vectors a · b= axbx + ayby + azbz to calculate the angle between the two vectors given by = 8.0i + 8.0j + 8.0k and = 7.0i + 5.0j + 6.0k.

The Attempt at a Solution

I found the magnitude of A = 11.3 and B = 8.6 using pythagorean theorem. Then I did 8x7 + 8x4 + 8x6 = 144. Then cos^-1(144/97.2), but I don't get an angle...

 

[tiny-tim]

Hi Gattz!

i] don't multiply the vectors by 4 at the start …

it makes the numbers too large …

find C.(AxB) first, then multiply it by -16.

Homework Equations

a x b = (a2b3 - a3b2) i + (a3b1 - a1b3) j + (a1b2 - a2b1) k

ii] yes, this is correct … use it! (for AxB)

(and don't bother with the (a1b2 - a2b1)k … you won't need it when you dot-product with C, will you? )

 

[tomcue]

Your approach to the first problem seems to be correct. However, your final answer should be in the form of a vector, not just a value. So the correct answer would be -4.00C * (224i + 1024j + 68k).

For the second problem, your approach is also correct. However, you made a mistake in calculating the magnitude of vector B. It should be 8.6, not 8.2. Also, when using the cosine function, make sure to use the inverse cosine function (cos^-1). So the final answer should be cos^-1 (144/97.2) = 51.3 degrees.