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

• bmchenry
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.
bmchenry

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

Is that the absolute value of A + B = 6?

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

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?

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?

Can you formulate the problem in a better way? For example you know that:

$$(B+1)^2 = 12$$

How would you solve that for B.

Never mind but thanks, I figured it out the answer is 3, but I need help bisecting a vector can you help?

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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