Question

The angle between the lines `vecr = (hati + 2hatj + 3hatk) + λ(2hati - 2hatj + hatk)` and `vecr = (hati + 2hatj + 3hatk) + µ(hati + 2hatj + 2hatk)` is ______.

Options

• `π/4`

• `π/2`

• `π/3`

• 0

Answer 1

The angle between the lines `vecr = (hati + 2hatj + 3hatk) + λ(2hati - 2hatj + hatk)` and `vecr = (hati + 2hatj + 3hatk) + µ(hati + 2hatj + 2hatk)` is `underlinebb(π/2)`.

Explanation:

Step 1: Direction vectors

From the equations:

Line 1 direction vector

`veca = (2, -2, 1)`

Line 2 direction vector

`vecb = (1, 2, 2)`

Step 2: Use formul

`cos θ = (veca * vecb)/(|veca||vecb|)`

Step 3: Find dot product

`veca * vecb = (2)(1) + (-2)(2) + (1)(2)`

= 2 – 4 + 2

= 0

Step 4: Since dot product = 0

cos θ = 0

`θ = π/2`