the angle between i +j and i is
a. pi/6
b. pi/2
c. pi/3
d. pi/2
i+j is at pi/4
i is at 0
I don't see a correct choice.
Now, if you are asking about +j and +i, that would be pi/2
k thx a lot
To find the angle between two vectors, you can use the dot product formula:
θ = arccos((A·B) / (|A| |B|))
In this case, the two vectors are i+j and i. Let's calculate it step by step:
1. Determine the dot product of the two vectors.
A·B = (1 * 1) + (1 * 0) = 1
2. Calculate the magnitudes of the two vectors.
|A| = √(1^2 + 1^2) = √2
|B| = √(1^2) = 1
3. Substitute the values into the formula and calculate the angle.
θ = arccos(1 / (√2 * 1)) = arccos(1 / √2) = arccos(1 / √2) / 1 = arccos(1 / √2)
To find the decimal value of the angle, we can use a calculator or approximate the value. Since arccos(1 / √2) is an inverse cosine function, we can evaluate it to get:
θ ≈ 0.7854 radians
Comparing this value to the given options, we see that option (a) pi/6 (which is approximately 0.5236 radians) is the closest option. So, the correct answer would be (a) pi/6.