Determine the value of k so that u=[2,5] and v=[k,4] are perpendicular.
If u and v are perpendicular then u•v = 0
[2,5]•[k,4] = 2k + 20
2k+20=0
k= -10
Well, awwfully hard to tell without a little assistance from trigonometr-ha! In order for two vectors to be perpendicular, their dot product must be zero. So, we can calculate the dot product of u and v and set it equal to zero to find the value of k.
The dot product of u and v is given by the formula u · v = (2)(k) + (5)(4) = 2k + 20. To make this equal to zero, we can set 2k + 20 equal to zero and solve for k.
2k + 20 = 0
Subtracting 20 from both sides gives us:
2k = -20
And finally, dividing both sides by 2, our final answer is:
k = -10
So, to make u and v perpendicular, the value of k must be -10. Let me tell you, that's one awkward angle!
To determine the value of k that makes vectors u=[2,5] and v=[k,4] perpendicular, we can use the dot product.
The dot product of two vectors is given by the formula:
u · v = u1 * v1 + u2 * v2
where u1 and u2 are the components of vector u, and v1 and v2 are the components of vector v.
In this case, the dot product of u and v must be equal to zero, since two vectors are perpendicular if and only if their dot product is zero.
u · v = 2 * k + 5 * 4 = 8 + 5k
Setting the dot product equal to zero:
8 + 5k = 0
Now, solve for k:
5k = -8
k = -8/5
Therefore, the value of k that makes vectors u=[2,5] and v=[k,4] perpendicular is k = -8/5.
To determine the value of k that makes vectors u and v perpendicular, we can use the properties of perpendicular vectors. Two vectors are perpendicular if their dot product is equal to zero.
The dot product of two vectors u and v is calculated by multiplying the corresponding components of the vectors and adding them up. In this case, the dot product of u and v is:
u · v = (2 * k) + (5 * 4)
To make the vectors perpendicular, their dot product should be equal to zero. Therefore, we can set up the equation:
(2 * k) + (5 * 4) = 0
Now we can solve for k:
2k + 20 = 0
Subtracting 20 from both sides:
2k = -20
Dividing both sides by 2:
k = -10
So, in order for vectors u and v to be perpendicular, the value of k should be -10.