EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Vector Algebra>JEE Advanced Paper 1 - 2018>Q 12

MEDIUM

JEE Advanced

IMPORTANT

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Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that $\vec{a} . \vec{b} = 0 .$ For some $x, y \in R,$ let $\vec{c} = x \vec{a} + y \vec{b} + (\vec{a} \times \vec{b}) .$ If $|\vec{c}| = 2$ and the vector $\vec{c}$ is inclined at the same angle $α$ to both $\vec{a}$ and $\vec{b},$ then the value of $8 \cos^{2} α$ is

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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 - 2015>Q 13

Let

Δ P Q R

be a triangle. Let

\vec{a} = \vec{Q R}, \vec{b} = \vec{R P} & \vec{c} = \vec{P Q}

. If

|\vec{a}| = 12, |\vec{b}| = 4 \sqrt{3}

and

\vec{b} \cdot \vec{c} = 24

, then which of the following is (are) true ?

HARD

JEE Advanced

IMPORTANT

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

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

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