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Expected value of exponential random variable

If an exponential random variable, X, has failure rate λ, what is E[X|X<λ]? I'm not sure how to start here. I know that E[X] = 1 / λ for an exponential random variable. Is the probability that X ...
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How to calculate whether a ray intersects an arbitrarily oriented bounding box?

The bounding box is not axis-aligned. It can be rotated. I now have the origin of the ray, and direction and each coordinate of the eight vertices of the bounding box. what can I do to find out this ...