Consider the following statements in respect of a vector \vec{d}=(\vec{a}\times\vec{b})\times\vec{c} : I. \vec{d} is coplanar with \vec{a} and \vec{b}. II. \vec{d} is perpendicular to \vec{c}. Which of the statements given above is/are correct?

Explanation

By the Vector Triple Product expansion, (\vec{a}\times\vec{b})\times\vec{c} = -\vec{c}\times(\vec{a}\times\vec{b}) = -[(\vec{c}\cdot\vec{b})\vec{a} - (\vec{c}\cdot\vec{a})\vec{b}]. Since \vec{d} is a linear combination of \vec{a} and \vec{b}, it lies in their plane (I is true). Also, the cross product of any two vectors is perpendicular to both, so \vec{d} \perp \vec{c} (II is true).

Related questions on Vector Algebra

• PQRS is a parallelogram. If \vec{PR}=\vec{a} and \vec{QS}=\vec{b}, then what is \vec{PQ} equal to?
• Let \vec{a} and \vec{b} are two unit vectors such that \vec{a}+2\vec{b} and 5\vec{a}-4\vec{b} are <strong>PERPENDICULAR</strong>. Wh...
• Let \vec{a}, \vec{b} and \vec{c} be unit vectors lying on the same <strong>COPLANAR</strong> plane. What is $\{(3\vec{a}+2\vec{b})\tim...
• What are the values of x for which the angle between the vectors 2x^{2}\hat{i}+3x\hat{j}+\hat{k} and \hat{i}-2\hat{j}+x^{2}\hat{k} is ...
• The position vectors of vertices A, B and C of triangle ABC are respectively \hat{j}+\hat{k}, 3\hat{i}+\hat{j}+5\hat{k} and $3\h...