Find a vector of magnitude 23 and which is perpendicular to each of the vectorà = 41 - 9+8k, b = -f+k.
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a vector of magnitude 23 and which is perpendicular to each of the vectorà = 41 - 9+8k, b = -f+k is -4i - 22.2j - 4k
Given,
à = 41 - 9+8k,
b = -f+k.
We have,
a = 41i - 9j + 8k
b = -i + k
a×b = (41i - 9j + 8k) × (-i + k) = -9i - 49j - 9k
|a×b| = √ [ (-9^2) + (-49^2) + (- 9)^2 ] = 50.62
A vector of magnitude 23
Therefore, the required vector is
= [ a×b / |a×b| ] × 23
= [ (-9i - 49j - 9k) / 50.62 ] × 23
= (-9i - 49j - 9k) (0.454)
= -4i - 22.2j - 4k
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