The scalar product of the vector $\hat{i}+\hat{j}+\hat{k}$ with a unit vector along the sum of the vectors $2\hat{i}+4\hat{j}-5\hat{k}$ and $\lambda\hat{i}+2\hat{j}+3\hat{k}$ is equal to 1, then value of $\lambda$ is
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Logic Tip: In vector equations leading to $\lambda + A = \sqrt{(.......)}$, squaring can sometimes introduce extraneous roots. Always double-check your final answer by substituting $\lambda=1$ back into the scalar product expression: $(3+6-2)/\sqrt{9+40} = 7/\sqrt{49} = 1$. The root is valid.