If and
they are perpendicular to each other.
Two vectors \(\vec{a}\) and \(\vec{b}\) are perpendicular to each other if their dot product is zero, i.e., \[ \vec{a} __________ __________ ___ ________ _____ ______ ___ _______ ____ ______ _________.
___ _________ __________ ____ _______ ____.
_____ _____ __________ _____ _________ ______ ___ ________ _____ __________.
_____ _____ _______ ___ ____ ___ ________.
_____ _______ _______ ____ __________ ______ _______ _________ _______ ________ _______.
_____ ________ ___ _____ _____ _________ __________ _________ ___ ________.
_____ ______ _______ __________ ___ ___ _________ ______ _________.
_________ _____ ______ _________ _____ ________ __________ ____ __________.
_________ _______ ______.
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In a factory there are three machines A, B, C which produce 10%, 40% and 50% items respectively. Past experience shows that percentage of defective items produced by machines A, B, C are 5%, 4%, 2% respectively. An item from the production of these machines is selected at random and it is found defective. What is the probability that it is produced by machine A?
If probability of an event E is 1/2 and probability of the event is 1/6, then probability of the event F is 1/3, where events E and F are independent.
If and
then find
.
A hospital specialising in heart surgery. In 2023 total of 1000 patients were admitted for treatment. The average payment made by a patient was Rs 1,00,000 with a standard deviation of Rs 20000. Under the assumption that payments follow a normal distribution, find the number of patients who paid between Rs 90,000 and Rs 1,10,000.
If and
they are perpendicular to each other.
Assume that in a population each person is equally likely to have a particular disease and disease status of each individual is independent of each other, then find the probability that out of the 5 randomly selected individuals who are tested for this particular disease exactly 3 have this disease.
Prove that is an orthogonal matrix.