Determine whether u and v are orthogonal,parallel, or neither.
u=-2i+j
v=3i+6j
To determine whether u and v are orthogonal, parallel, or neither, we need to calculate their dot product.
The dot product of two vectors u and v is calculated using the formula:
u · v = (u1 * v1) + (u2 * v2)
Let's calculate the dot product of u and v:
u · v = (-2 * 3) + (1 * 6)
= -6 + 6
= 0
The dot product of u and v is 0.
Since the dot product of u and v is 0, we can conclude that u and v are orthogonal vectors.
To determine whether the vectors u and v are orthogonal, parallel, or neither, we can use the dot product of the two vectors.
The dot product of two vectors u and v is calculated by multiplying the corresponding components of the two vectors and then summing the results.
The dot product formula is: u • v = (u1 * v1) + (u2 * v2) + ... + (un * vn)
Let's calculate the dot product of u and v.
u = -2i + j
v = 3i + 6j
u • v = (-2 * 3) + (1 * 6)
= -6 + 6
= 0
Since the dot product of u and v is zero, we can conclude that u and v are orthogonal.