(c) A vector contains an unknown real number

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

\vec{u}=x\,\hat{i}+2\,\hat{j}-\hat{k}

contains an unknown real number

x

. Another vector is

\vec{v}=3\,\hat{i}-\hat{j}+4\,\hat{k}

. It is known that the component of

\vec{u}\times\vec{v}

along

\hat{k}

equals

20

. (i) Without expanding completely, write

\vec{u}\times\vec{v}

as a

3\times3

determinant. (ii) Evaluate the determinant to obtain each component of

\vec{u}\times\vec{v}

in terms of

x

. (iii) Using the condition on the

\hat{k}

-component, determine the value of

x

. (iv) Substitute this value back to write the complete vector

\vec{u}\times\vec{v}