A=3i + 2j +k and Bz = -1i +2j +Bk. |A + B| =6. Find Bk

  • Thread starter bmchenry
  • Start date
In summary, the problem involves finding two possible values for Bz when given two vectors A and B and the absolute value of their sum is equal to 6. The first value of Bz is -4.87, but the second value is incorrect. The mistake lies in not considering the term (1+B)^2 when adding the vectors, and the correct answer is 3. Another problem involving bisecting a vector is mentioned, but the solution is not provided.
  • #1
bmchenry
10
0

Homework Statement



2 vectors are given by A=3i + 2j +k and Bz = -1i +2j +Bk. A + B =6

Homework Equations



Find the two possible vlaues of Bz

The Attempt at a Solution



6 = sqrt (4 + 20 +Bzsquared)

I get one number to equal -4.87 but when I solve for the other I get it wrong on the online check
 
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  • #2
Is that the absolute value of A + B = 6?
 
  • #3
yes it is the absolute value 6, I thought the answer would be to just take the positive 3.87 and subtract 1 from it but that was wrong online
 
  • #4
Ok well in the equation you've come up with you wouldn't just have B2. When you add the vectors you would end up with a term (1+B)2. What values can B take to make everything under square root add up to 36?
 
  • #5
Did that and for one answer I got -4.87 which when you put it in the () and square it you get 36 or close enough that the online problem accepted the answer, I assumed that for the other number I just needed to take 3.87 and subtract the 1 which left me with 2.87, however when I plug that in it says it is incorrect, where is my mistake?
 
  • #6
Can you formulate the problem in a better way? For example you know that:

[tex] (B+1)^2 = 12[/tex]

How would you solve that for B.
 
  • #7
Never mind but thanks, I figured it out the answer is 3, but I need help bisecting a vector can you help?
 
  • #8
3? I would not have thought it would be, but the online thing might be accepting answers within certain ranges. It would be best to post a new thread to receive the maximum attention.
 

1. What is the formula for vector addition?

The formula for vector addition is A + B = (A_x + B_x)i + (A_y + B_y)j + (A_z + B_z)k.

2. How do you find the magnitude of a vector?

The magnitude of a vector is found by taking the square root of the sum of the squares of its components. In this case, |A + B| = sqrt[(3+(-1))^2 + (2+2)^2 + (1+B)^2] = 6. Expanding this equation, we get (2)^2 + (4)^2 + (1+B)^2 = 36. Solving for B, we get B = 3 or -5.

3. How do you represent a vector in its component form?

A vector in its component form is written as A = A_xi + A_yj + A_zk. This represents the vector's magnitude and direction in the x, y, and z directions respectively.

4. What is the significance of the i, j, and k unit vectors?

The i, j, and k unit vectors represent the standard unit vectors in the x, y, and z directions respectively. They are used to indicate the direction of a vector's components and are crucial in vector calculations and representations.

5. How do you calculate the dot product of two vectors?

The dot product of two vectors A and B is calculated by multiplying their corresponding components and taking the sum of these products. In this case, A * B = (3*(-1)) + (2*2) + (1*B) = -3 + 4 + B = B + 1.

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