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यदि मूल बिन्दु $\mathrm{O}$ हो तथा $\overline{\mathrm{OP}}=2 \hat{i}+3 \hat{j}-4 \hat{k}$ तथा $\overline{\mathrm{OQ}}=5 \hat{i}+4 \hat{j}-3 \hat{k}$ हों, तो $\overline{\mathrm{PQ}}$ समान है :
यदि $\vec{a}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$ और $\overrightarrow{\mathrm{b}}=3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}$ तो $(\vec{a}+3 \overrightarrow{\mathrm{b}}) \cdot(2 \overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}})$ का मान है :