IIT-JEE 2008 Paper 2 Offline | Vector Algebra Question 41 | Mathematics

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let two non-collinear unit vectors $$\widehat a$$ and $$\widehat b$$ form an acute angle. A point $$P$$ moves so that at any time $$t$$ the position vector $$\overrightarrow {OP} $$ (where $$O$$ is the origin) is given by $$\widehat a\cos t + \widehat b\sin t.$$ When $$P$$ is farthest from origin $$O,$$ let $$M$$ be the length of $$\overrightarrow {OP} $$ and $$\widehat u$$ be the unit vector along $$\overrightarrow {OP} $$. Then :

$$\widehat u = {{\widehat a + \widehat b} \over {\left| {\widehat a + \widehat b} \right|}}\,\,and\,\,M = {\left( {1 + \widehat a.\,\widehat b} \right)^{1/2}}$$

$$\widehat u = {{\widehat a - \widehat b} \over {\left| {\widehat a - \widehat b} \right|}}\,\,and\,\,M = {\left( {1 + \widehat a.\,\widehat b} \right)^{1/2}}$$

$$\widehat u = {{\widehat a + \widehat b} \over {\left| {\widehat a + \widehat b} \right|}}\,\,and\,\,M = {\left( {1 + 2\widehat a.\,\widehat b} \right)^{1/2}}$$

$$\widehat u = {{\widehat a - \widehat b} \over {\left| {\widehat a - \widehat b} \right|}}\,\,and\,\,M = {\left( {1 + 2\widehat a.\,\widehat b} \right)^{1/2}}$$

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-1

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$ such that $$\widehat a\,.\,\widehat b = \widehat b\,.\,\widehat c = \widehat c\,.\,\widehat a = {1 \over 2}.$$ Then, the volume of the parallelopiped is :

$${1 \over {\sqrt 2 }}$$

$${1 \over {2\sqrt 2 }}$$

$${{\sqrt 3 } \over 2}$$

$${1 \over {\sqrt 3 }}$$

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

-1

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

$$\vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a}=\overrightarrow{0}$$

$$\vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a} \neq \overrightarrow{0}$$

$$\vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{a} \times \vec{c} \neq \overrightarrow{0}$$

$$\vec{a} \times \vec{b}, \vec{b} \times \vec{c}, \vec{c} \times \vec{a}$$ are mutually perpendicular

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-1

The number 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

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