If a vector 2i+3j+8k is perpendicular to the vector 4j−4i+alpha k then the value of alpha is? solve without using the property of dot product.

Bodonimhk 2022-10-13 Answered
If a vector 2 i + 3 j + 8 k is perpendicular to the vector 4 j 4 i + α k then the value of α is? solve without using the property of dot product.
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Answers (2)

periasemdy
Answered 2022-10-14 Author has 15 answers
Since the two vectors are perpendicular, a less natural way would be think of Pythagoras theorem
Let A B = 2 i + 3 j + 8 k and A C = 4 i + 4 j + α k
Since A B A C , Therefore we have B C = A C A B = 6 i + j + ( α 8 ) k
Also B C 2 = A C 2 + A B 2
( 6 ) 2 + ( 1 ) 2 + ( α 8 ) 2 = ( 16 + 16 + α 2 ) + ( 4 + 9 + 64 )
α = 0.5
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4enevi
Answered 2022-10-15 Author has 5 answers
You can use the Pythagorean theorem. If you add two vectors, you get 6 i j + ( 8 + α ) k. Then we have
36 + 1 + ( 8 + α ) 2 = 4 + 9 + 64 + 16 + 16 + α 2 16 α = 8
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