To determine the projection of 2a b→ →+ on a→, we need to find the component of 2a b→ →+ that lies in the same direction as a→.

First, let's find the unit vector in the direction of a→. We can do this by dividing a→ by its magnitude.

The magnitude of a→ is given by |a→| = √(2^2 + 3^2 + 2^2) = √17.

So, the unit vector in the direction of a→ is given by a→/|a→| = (-2/√17)i + (3/√17)j + (2/√17)k.

Next, we need to find the dot product of 2a b→ →+ and the unit vector in the direction of a→.

The dot product is given by (2a b→ →+) · (a→/|a→|) = 2a b→ →+ · (-2/√17)i + (3/√17)j + (2/√17)k.

Expanding this, we get (2a b→ →+) · (-2/√17)i + (3/√17)j + (2/√17)k = (-4a/√17) + (6b/√17) + (4a/√17).

Simplifying further, we have (-4a/√17) + (6b/√17) + (4a/√17) = (2b/√17).

Therefore, the projection of 2a b→ →+ on a→ is given by (2b/√17).

Question

To determine the projection of 2a b→ →+ on a→, we need to find the component of 2a b→ →+ that lies in the same direction as a→.

First, let's find the unit vector in the direction of a→. We can do this by dividing a→ by its magnitude.

The magnitude of a→ is given by |a→| = √(2^2 + 3^2 + 2^2) = √17.

So, the unit vector in the direction of a→ is given by a→/|a→| = (-2/√17)i + (3/√17)j + (2/√17)k.

Next, we need to find the dot product of 2a b→ →+ and the unit vector in the direction of a→.

The dot product is given by (2a b→ →+) · (a→/|a→|) = 2a b→ →+ · (-2/√17)i + (3/√17)j + (2/√17)k.

Expanding this, we get (2a b→ →+) · (-2/√17)i + (3/√17)j + (2/√17)k = (-4a/√17) + (6b/√17) + (4a/√17).

Simplifying further, we have (-4a/√17) + (6b/√17) + (4a/√17) = (2b/√17).

Therefore, the projection of 2a b→ →+ on a→ is given by (2b/√17).

Knowee AI · Accepted Answer