The vectors 2,i + 3,j - 4,k and a,i + b,j + c | vedclass

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(B) Two vectors $\vec{A} = A_1\,i + A_2\,j + A_3\,k$ and $\vec{B} = B_1\,i + B_2\,j + B_3\,k$ are perpendicular if and only if their dot product is ze

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$a = 4, b = 4, c = 5$

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(B) Two vectors $\vec{A} = A_1\,i + A_2\,j + A_3\,k$ and $\vec{B} = B_1\,i + B_2\,j + B_3\,k$ are perpendicular if and only if their dot product is zero,i.e.,$\vec{A} \cdot \vec{B} = 0$. Given vectors are $\vec{A} = 2\,i + 3\,j - 4\,k$ and $\vec{B} = a\,i + b\,j + c\,k$. The condition for perpendicularity is $(2)(a) + (3)(b) + (-4)(c) = 0$,which simplifies to $2a + 3b - 4c = 0$. Checking option $(b)$: $2(4) + 3(4) - 4(5) = 8 + 12 - 20 = 20 - 20 = 0$. Since the dot product is $0$,the vectors are perpendicular for the values given in option $(b)$.

The vectors $2\,i + 3\,j - 4\,k$ and $a\,i + b\,j + c\,k$ are perpendicular,when

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