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.