The line of intersection of the planes ${\bf{\vec r}}\,\, \cdot \,\,\left( {\widehat {{\bf{\dot i}}} - 3\widehat {\,{\bf{\dot j}}} + {\bf{\hat k}}} \right) = 1$ and ${\bf{\vec r}}\,\, \cdot \,\,\left( {2\,\widehat {{\bf{\dot i}}} + 5\,\widehat {{\bf{\dot j}}} - 3\,{\bf{\hat k}}} \right) = 2$ is parallel to the vector

$4\widehat {\,{\bf{\dot i}}} + 5\widehat {\,{\bf{\dot j}}} + 11\,{\bf{\hat k}}$

$ - \,4\,\widehat {{\bf{\dot i}}} + 5\widehat {\,{\bf{\dot j}}} + 11\,{\bf{\hat k}}$

$ - \,4\,\widehat {{\bf{\dot i}}} - 5\widehat {\,{\bf{\dot j}}} + 11\,{\bf{\hat k}}$

$ - \,4\,\widehat {{\bf{\dot i}}} + 5\,\widehat {{\bf{\dot j}}} - 11\,{\bf{\hat k}}$

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

1 of 1

Application +4 | -1

The line of intersection of the planes

\mathbf{\vec r}\,\, \cdot \,\,\left( {\widehat {\mathbf{\dot i}} - 3\widehat {\,\mathbf{\dot j}} + \mathbf{\hat k}} \right) = 1

and

\mathbf{\vec r}\,\, \cdot \,\,\left( {2\,\widehat {\mathbf{\dot i}} + 5\,\widehat {\mathbf{\dot j}} - 3\,\mathbf{\hat k}} \right) = 2

is parallel to the vector

View answer and explanation

Correct option: B

4\widehat {\,\mathbf{\dot i}} + 5\widehat {\,\mathbf{\dot j}} + 11\,\mathbf{\hat k}

Option B (

4\widehat {\\,\mathbf{\dot i}} + 5\widehat {\\,\mathbf{\dot j}} + 11\mathbf{\hat k}

) is correct because it is the cross product of the normal vectors of the two planes, which gives the direction vector of the line of intersection.