If vector |a| = 12 cm, |b| = 13 cm, and the angle between them when placed tail to tail is 35°, find a • b to the nearest centimetre
a)
a • b = 57
b)
a • b = 8
c)
a • b = 11
d)
a • b = 24
Tail to tail, the dot product is
12 * 13 cos 35 = 127.78 cm^2
Round that off as requested. It is an area, not a length.
Hey there! Ready for some funny math? Let's calculate a • b!
First, we need to find the magnitude of the dot product between a and b. We can use the formula:
a • b = |a| |b| cos(theta)
where |a| is the magnitude of vector a, |b| is the magnitude of vector b, and theta is the angle between them.
In this case, |a| = 12 cm, |b| = 13 cm, and the angle theta = 35°.
Plugging these values into the formula, we get:
a • b = 12 cm * 13 cm * cos(35°)
Now, I'm not an expert on trigonometry, but I can tell you that cos(35°) is approximately 0.819.
So, a • b is approximately:
a • b ≈ 12 cm * 13 cm * 0.819 ≈ 127.956 cm
Now, since we want to round it to the nearest centimeter, the answer is approximately 128 cm.
Wait, before you ask, no, I don't know why a banana can't feel its own hair. It's just a different kind of math!
So, based on the multiple choice options, the closest answer is:
a) a • b ≈ 57 cm
Hope that brings a smile to your face!
To find a • b (the dot product of vectors a and b), we can use the formula:
a • b = |a| * |b| * cos(theta)
Where |a| and |b| are the magnitudes of vectors a and b, and theta is the angle between them.
Given that |a| = 12 cm, |b| = 13 cm, and the angle between them is 35°, we can substitute these values into the formula:
a • b = 12 cm * 13 cm * cos(35°)
Using a calculator, we can calculate cos(35°) ≈ 0.819152044.
a • b = 12 cm * 13 cm * 0.819152044 ≈ 127.7482356
Rounding this to the nearest centimeter, we get a • b ≈ 128.
Therefore, the correct answer is:
a) a • b = 128
To find the dot product (a • b) of two vectors a and b, you can use the formula:
a • b = |a| * |b| * cos(θ)
Where |a| and |b| represent the magnitudes (lengths) of vectors a and b, and θ is the angle between them.
In this case, you are given:
|a| = 12 cm,
|b| = 13 cm,
and the angle between them (θ) is 35°.
Plug these values into the formula to calculate a • b:
a • b = 12 cm * 13 cm * cos(35°)
Now, calculate cos(35°) using a calculator:
cos(35°) ≈ 0.819
Substitute this value back into the equation:
a • b ≈ 12 cm * 13 cm * 0.819
Now, multiply the values to obtain the dot product:
a • b ≈ 121.212 cm²
To the nearest centimeter, the dot product (a • b) is approximately 121 cm².
Therefore, the answer is option d) a • b = 24.