When is it necessary to use a hyphen in writing a compound word?
To hyphenate or not?
Which one is correct?
The normal vector we mean is the inward-pointing normal.
The normal vector we mean is the inward pointing normal.
Which one is correct?
First let me state that this is mostly a matter of style, and if you are writing for an academic or technical publication, you would do well to get a copy of their style guide and look there for your answer.
That said, hyphens in compound adjectives are used for clarity. They are not always necessary, but are used when a compound may be ambiguous, as in
Here the first sentence could mean an auction of small cars or a car auction that is small. The second sentence specifies that it is the former.
When an adverb and adjective combine to make a compound adjective, a hyphen is frequently unnecessary, because more often there is less chance for ambiguity.
Here there is little chance for confusion, so the hyphen may be dropped.
In your example, "inward pointing" and "inward-pointing" are both correct and easily understood. It becomes a matter of style as to which you prefer.
The general rule is: When you have a pattern like "adjective noun noun", hyphenate the first two words if the adjective modifies the immediately following noun; do not hyphenate if the adjective modifies the second noun.
As in Mr Robusto's example, a "small-car auction" is an auction of small cars, while a "small car auction" is a small auction of (any-sized) cars.
I'd differ with Mr Robusto in that I really think you should always use the hyphen when it applies. Yes, there are cases where one combination would not make sense and so there is no ambiguity. But it's better to be consistent rather than try to turn every use into a unique case to be considered from scratch. I can't think of any advantage gained by leaving out the hyphen, so rather than contemplate every use, just do it. If you try to think out each case, not only do you waste time and effort, but sooner or later you will create an ambiguity because you didn't happen to think of an alternate reading.
It's like driving on the correct side of the road. Sure, if no one's coming the other way, it might be safe to violate this rule sometimes. But what if you make a habit of driving on the wrong side of the road whenever it "looks safe", sooner or later someone will suddenly come around a corner, or you won't see the other car because of the rain or fog, or you'll just be distracted and not notice. What's the gain? If you truly come across a case where the hyphen hurts readabiliity, sure, drop it. But I think such cases are rarer than legitimate cases for briefly driving on the wrong side of the road (like there's a huge pot hole, or a child playing in the street).