Consider the two vectors a⃗ = 2î - 3ĵ + 4k̂ and b⃗ = 5î + qĵ - k̂. Calculate 'q' if both the vectors are perpendicular to each other.

The vectors are perpendicular, so a⃗·b⃗ = 0: 2(5) + (-3)(q) + 4(-1) = 0, so 10 - 3q - 4 = 0 and q = 2. 2

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Consider the two vectors a⃗ = 2î - 3ĵ + 4k̂ and b⃗ = 5î + qĵ - k̂. Calculate 'q' if both the…

Consider the two vectors $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{b} = 5\hat{i} + q\hat{j} - \hat{k}$. Calculate '$q$' if both the vectors are perpendicular to each other.

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Answer

The vectors are perpendicular, so $\vec{a}\cdot\vec{b} = 0$: $2(5) + (-3)(q) + 4(-1) = 0$, so $10 - 3q - 4 = 0$ and $q = 2$.

Final answer: $2$