If the vectors A = 3i-j and B= 2i+kj
are parallel, the scalar k is equal to :
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Answer:
using dot product.
when two vectors are parallel their dot product is equal to product of their magnitudes.
that means,
A•B=|A|.|B|
(3i-j)•(2i+kj)=|3i-j||2i+kj|
6-k=(√3²+1²)(√2²+k²)
6-k=(√10)(√4+k²)
(6-k)²=40+10k²
36+k²-12k=40+10k²
9k²+12k=-4
(3k)²+2*3k*2+4=-4+4
(3k+2)²=0
3k+2=0
k=-2/3.
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