Let $ \overrightarrow{\mathrm{c}} $ be a vector perpendicular to the vectors $ \overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\widehat{\mathrm{k}} $ and $ \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\widehat{\mathrm{k}} $ If $ \overrightarrow{\mathrm{c}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \widehat{\mathrm{k}})=8 $ then the value of $ \overrightarrow{\mathrm{c}} \cdot(\vec{a} \times \vec{b}) $ is equal to

Question

Let $ \overrightarrow{\mathrm{c}} $ be a vector perpendicular to the vectors $ \overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\widehat{\mathrm{k}} $ and $ \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\widehat{\mathrm{k}} $ If $ \overrightarrow{\mathrm{c}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \widehat{\mathrm{k}})=8 $ then the value of $ \overrightarrow{\mathrm{c}} \cdot(\vec{a} \times \vec{b}) $ is equal to,

MARKS App · Accepted Answer

c → = λ ( a → × b → ) a → × b → = i ^ j ^ k ^ 1 1 - 1 1 2 1 ( a → × b → ) = 3 i ^ - 2 j ^ + k ^ c → · ( i ^ + j ^ + 3 k ^ ) = λ ( 3 i ^ - 2 j ^ + k ^ ) · ( i ^ + j ^ + 3 k ^ ) ⇒ λ ( 4 ) = 8 ⇒ λ = 2 c → = 2 ( a → × b → )

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