As z1 = 3 - 4i and z2 = -4 + 3i, then the acute angle between the vectors will be?
- 18°16'
- 17°16'
- 16°16'
- None of these
Explanation
To find the acute angle between the vectors, first find the dot product:
z1 = 3 - 4i
z2 = -4 + 3i
Dot product = (3)(-4) + (-4)(3) = -12 - 12 = -24
Next, find the magnitudes:
|z1| = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5
|z2| = √((-4)^2 + 3^2) = √(16 + 9) = √25 = 5
Now, find the cosine of the angle:
cos(θ) = (Dot product) / (|z1| |z2|)
= -24 / (5 * 5)
= -24 / 25
θ = arccos(-24/25) ≈ 16°16'
Related MCQs
- Odd function
- Even function
- Constant symmetric form
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- Factoring the polynomial
- Finding the derivative
- Substituting the value of x
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- x = 2, −1/2
- x = 1, −2
- x = 3, −1
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- Commutative
- Associative
- Distributive
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
