I want b solve b

Question

I want b solve b

ScanSolve AI Tutor · Accepted Answer

Okay, Tfrey, let's solve part b).

The problem states that vectors $\mathbf{a} = \begin{bmatrix} 2 \\ k \\ -3 \end{bmatrix}$ and $\mathbf{b} = \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix}$ are perpendicular. We need to find the value of $k$ .

Recall the condition for perpendicular vectors.
Two vectors are perpendicular if their dot product is zero.
$\mathbf{a} \cdot \mathbf{b} = 0$
Calculate the dot product of $\mathbf{a}$ and $\mathbf{b}$ .
The dot product is calculated by multiplying corresponding components and summing the results.
$\mathbf{a} \cdot \mathbf{b} = (2)(4) + (k)(-2) + (-3)(1)$ $\mathbf{a} \cdot \mathbf{b} = 8 - 2k - 3$
Set the dot product equal to zero and solve for $k$ .
$8 - 2k - 3 = 0$ $5 - 2k = 0$ $5 = 2k$ $k = \frac{5}{2}$
The value of $k$ is:
$\frac{5}{2}$

I want b solve b

Answer

Step-by-step solution

Recall the condition for perpendicular vectors.

Calculate the dot product of $\mathbf{a}$ and $\mathbf{b}$ .

Set the dot product equal to zero and solve for $k$ .

Try one yourself

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I want b solve b

Answer

Step-by-step solution

Recall the condition for perpendicular vectors.

Calculate the dot product of a\mathbf{a}a and b\mathbf{b}b.

Set the dot product equal to zero and solve for kkk.

Try one yourself

Still stuck on this one?

More Physics Questions

Calculate the dot product of $\mathbf{a}$ and $\mathbf{b}$ .

Set the dot product equal to zero and solve for $k$ .