EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Vector Algebra>JEE Advanced Paper 1 - 2014>Q 14

HARD

JEE Advanced

IMPORTANT

Earn 100

Let $\vec{x}, \vec{y}$ and $\vec{z}$ be three vectors each of magnitude $\sqrt{2}$ and the angle between each pair of them is $\frac{π}{3} .$ If $\vec{a}$ is a non - zero vector perpendicular to $\vec{x}$ and $\vec{y} \times \vec{z}$ and $\vec{b}$ is a non - zero vector perpendicular to $\vec{y}$ and $\vec{z} \times \vec{x}$ , then

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Important Questions on Vector Algebra

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Vector Algebra>JEE Advanced Paper 1 - 2013>Q 16

Let

\vec{P R} = 3 \hat{i} + \hat{j} - 2 \hat{k} & \vec{S Q} = \hat{i} - 3 \hat{j} - 4 \hat{k}

determine diagonals of a parallelogram

P Q R S

and

\vec{P T} = \hat{i} + 2 \hat{j} + 3 \hat{k}

be another vector. Then the volume (in cubic unit) of the parallelepiped determined by the vectors

\vec{P T}, \vec{P Q} & \vec{P S}

is

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Vector Algebra>JEE Advanced Paper 2 - 2020>Q 2

Let

a

and

b

be positive real numbers. Suppose

\vec{P Q} = a \hat{i} + b \hat{j}

and

\vec{P S} = a \hat{i} - b \hat{j}

are adjacent sides of a parallelogram

P Q R S .

Let

\vec{u}

and

\vec{v}

be the projection vectors of

\vec{w} = \hat{i} + \hat{j}

along

\vec{P Q}

and

\vec{P S}

, respectively. If

| \vec{u} | + |\vec{v}| = |\vec{w}|

and if the area of the parallelogram

P Q R S

is

8 Sq. unit,

then which of the following statements is/are TRUE?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Vector Algebra>JEE Advanced Paper 1 - 2020>Q 11

In a triangle $P Q R$ , let $\vec{a} = \vec{Q R}, \vec{b} = \vec{R P}$ and $\vec{c} = \vec{P Q}$ .

If $|\vec{a}| = 3, |\vec{b}| = 4$ and $\frac{\vec{a} . (\vec{c} - \vec{b})}{\vec{c} . (\vec{a} - \vec{b})} = \frac{|\vec{a}|}{|\vec{a}| + |\vec{b}|}$ , then the value of ${|\vec{a} \times \vec{b}|}^{2}$ is _______