If the vectors hat{i}+3 hat{j}+4 hat{k} and l | vedclass

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(C) Let $\vec{a} = \hat{i} + 3\hat{j} + 4\hat{k}$ and $\vec{b} = \lambda\hat{i} - 4\hat{j} + \hat{k}$.Since the vectors $\vec{a}$ and $\vec{b}$ are or

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$8$

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(C) Let $\vec{a} = \hat{i} + 3\hat{j} + 4\hat{k}$ and $\vec{b} = \lambda\hat{i} - 4\hat{j} + \hat{k}$.Since the vectors $\vec{a}$ and $\vec{b}$ are orthogonal,their dot product must be zero,i.e.,$\vec{a} \cdot \vec{b} = 0$.Calculating the dot product:$(\hat{i} + 3\hat{j} + 4\hat{k}) \cdot (\lambda\hat{i} - 4\hat{j} + \hat{k}) = 0$$(1)(\lambda) + (3)(-4) + (4)(1) = 0$$\lambda - 12 + 4 = 0$$\lambda - 8 = 0$$\lambda = 8$.

If the vectors $\hat{i}+3 \hat{j}+4 \hat{k}$ and $\lambda \hat{i}-4 \hat{j}+\hat{k}$ are orthogonal to each other,then $\lambda$ is equal to:

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