IIT-JEE 2007 | Vector Algebra Question 1 | Mathematics

IIT-JEE 2007

MCQ (Single Correct Answer)

-0.75

Let the vectors $$\overrightarrow {PQ} ,\,\,\overrightarrow {QR} ,\,\,\overrightarrow {RS} ,\,\,\overrightarrow {ST} ,\,\,\overrightarrow {TU} ,$$ and $$\overrightarrow {UP} ,$$ represent the sides of a regular hexagon.

STATEMENT-1: $$\overrightarrow {PQ} \times \left( {\overrightarrow {RS} + \overrightarrow {ST} } \right) \ne \overrightarrow 0 .$$ because
STATEMENT-2: $$\overrightarrow {PQ} \times \overrightarrow {RS} = \overrightarrow 0 $$ and $$\overrightarrow {PQ} \times \overrightarrow {ST} \ne \overrightarrow 0 \,\,.$$

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Statement-1 is True, Statement-2 is False

Statement-1 is False, Statement-2 is True.

IIT-JEE 2007

MCQ (Single Correct Answer)

-0.75

Let $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$ be unit vectors such that $${\overrightarrow a + \overrightarrow b + \overrightarrow c = \overrightarrow 0 .}$$ Which one of the following is correct ?

$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a = \overrightarrow 0 $$

$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a \ne \overrightarrow 0 $$

$$\overrightarrow a \times \overrightarrow b = b \times \overrightarrow c = \overrightarrow a \times \overrightarrow c \ne \overrightarrow 0 $$

$$\overrightarrow a \times \overrightarrow b ,b \times \overrightarrow c ,\overrightarrow c \times \overrightarrow a $$ are muturally perpendicular

IIT-JEE 2007

MCQ (Single Correct Answer)

-0.75

The minimum of distinct real values of $$\lambda ,$$ for which the vectors $$ - {\lambda ^2}\widehat i + \widehat j + \widehat k,$$ $$\widehat i - {\lambda ^2}\widehat j + \widehat k$$ and $$\widehat i + \widehat j - {\lambda ^2}\widehat k$$ are coplanar, is

zero

one

two

three

JEE Advanced 2026 Paper 2 Online

MCQ (Single Correct Answer)

-1

Let $ \vec{a}, \vec{b} $ be two vectors, and let P, Q and R be the points with position vectors $ \vec{a}, \vec{b} $ and $ \vec{a} + \vec{b} $, respectively, with respect to the origin O. If $ |\vec{a} + \vec{b}| = \sqrt{21} $, $ |\vec{a} - \vec{b}| = 3 $, and $ \vec{a} $ and $ (\vec{a} - \vec{b}) $ are perpendicular to each other, then the area of the triangle OPR is :

$ \sqrt{3} $

$ \frac{\sqrt{3}}{2} $

$ \frac{3\sqrt{3}}{2} $

$ \frac{3}{2} $

JEE Advanced Subjects

Browse all chapters by subject