find a vector in the opposite direction of the vector a=3i-2j-9k that has magnitude of 5.
Answers
Answer:
Find a vector whose magnitude is 7 and which is perpendicular to each vector A = 2i - 3j + 6k and vector B = i + j - k ?
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The cross product of any two vectors will be perpendicular to both the vectors.
To solve this problem, first you have to find the cross product A⃗ X B⃗ . Then find the magnitude of this vector. If it is 7, you have your answer. If it is not 7, what you have to do is divide the vector by its magnitude, and multiply it by 7.
A⃗ =2i^−3j^+6k^
B⃗ =i^+j^−k^
A⃗ X B⃗ =−3i^+8j^+5k^
|A⃗ X B⃗ | = (−3)2+82+52−−−−−−−−−−−−−√ = 98−−√ = 72–√
Therefore required vector is : A⃗ XB⃗ |A⃗ XB⃗ |∗7 = −3i^+8j^+5k^72–√∗7 = −3i^+8j^+5k^2–√
If multiply this vector by (-1), it would still have the same magnitude, at the same time, it would be perpendicular to A⃗ & B⃗ . Hence 3i^−8j^−5k^2–√ is also correct.