If Ā = 3î + 4j − 5k and = 5î + 4j − 3k then Ā∙B = ___
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Consider the vector
A
=2i^+3j^−4k^
And B
=5i^+2j^+4k^
Now, as we know
A
.B
=ABcosθ
θ is the angle between A
and B
Therefore,
cosθ=ABA
.B
cosθ=22+32+(−4)2
52+22+42
(2i^+3j^−4k^).(5i^+2j^+4k^)
=22+32+(−4)2
52+22+42
(10+6−16)=0
Therefore, cosθ=0
θ=90∘
Hence angle between the vectors is 90∘.
Step-by-step explanation:
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