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Question
The angle between the planes `vecr.(2hati - 3hatj + hatk)` = 1 and `vecr.(hati - hatj)` = 4 is `cos^-1((-5)/sqrt(58))`.
Options
True
False
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Solution
This statement is True.
Explanation:
`vecb_1 = 2hati - 3hatj + hatk, vecb_2 = hati - hatj`
`cos theta = (|vecb_1 * vecb_2|)/(|vecb_1|*|vecb_2|)`
`cos theta = (|(2hati - 3hatj + hatk)*(hati - hatj)|)/(|2hati - 3hatj + hatk|*|hati - hatj|)`
= `(2 xx 1 - 3(-1) + (0))/(sqrt(4 + 9 + 1) * sqrt(1 + 1))`
= `(|2 + 3 + 0|)/(sqrt(4)*sqrt(2))`
= `5/sqrt(28)`.
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