If Vector a = (2, 2k), Vector b = (4, -k), are perpendicular, solve for k
with full solutions?
a dot b must be zero. Right?
2*4+2(-k)=0
oops
2*4+ 2k(-k)=0
To check if two vectors are perpendicular, we can use the dot product.
The dot product of two vectors a = (a₁, a₂) and b = (b₁, b₂) is given by:
a · b = a₁ * b₁ + a₂ * b₂
If a · b = 0, then the vectors a and b are perpendicular.
Let's find the dot product of vectors a and b:
a · b = (2 * 4) + (2k * -k)
= 8 - 2k²
Since we know that a · b = 0 because the vectors are perpendicular, we can solve the equation:
8 - 2k² = 0
Rearranging the equation, we have:
2k² = 8
Divide both sides by 2:
k² = 4
Taking the square root of both sides:
k = ±2
Therefore, the value of k can be either 2 or -2.
Thus, the possible solutions for k are k = 2 and k = -2.