A vector (d) is equally inclined to three vectors \( \mathbf{a}=\ha...

A vector (d) is equally inclined to three vectors \( \mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}} \) and \( \mathbf{c}=3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}} \). Let \( x, y, z \) be three vectors in the plane of \( a, b ; b, c, c \), respectively, then
(a) \( x \cdot d=14 \)
(b) \( y \cdot d=3 \)
(c) \( z \cdot d=0 \)
(d) \( \mathbf{r} \cdot \mathbf{d}=0 \), where \( \mathbf{r}=\lambda x+\mu y+\delta z \)