In a triangle A B C , right angle at vertex A , if the position vectors of A , B and C are respectively 3 i ^ + j ^ - k ^ , - i ^ + 3 j ^ + p k ^ and 5 i ^ + q j ^ - 4 k ^ , then the point p , q lies on a line:

Making an acute angle with the positive direction of x - a x i s

Making an obtuse angle with the positive direction of x - a x i s

In a triangle A B C , right angle at vertex A , if the position vectors of A , B and C are respectively 3 i ^ + j ^ - k ^ , - i ^ + 3 j ^ + p k ^ and 5 i ^ + q j ^ - 4 k ^ , then the point p , q lies on a line:

Making an acute angle with the positive direction of x - a x i s

Let a → = 5 i ^ - j ^ - 3 k ^ and b → = i ^ + 3 j ^ + 5 k ^ be two vectors. Then which one of the following statements is TRUE?

Projection of a → on b → is - 13 35 and the direction of the projection vector is opposite to the direction of b →

Projection of a → on b → is - 17 35 and the direction of the projection vector is opposite to the direction of b →

Projection of a → on b → is 17 35 and the direction of the projection vector is opposite to the direction of b →

Projection of a → on b → is 13 35 and the direction of the projection vector is opposite to the direction of a →

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 9th April 2016>Q 75

HARD

JEE Main

IMPORTANT

Earn 100

In a triangle $A B C$ , right angle at vertex $A$ , if the position vectors of $A, B$ and $C$ are respectively $3 \hat{i} + \hat{j} - \hat{k}, - \hat{i} + 3 \hat{j} + p \hat{k}$ and $5 \hat{i} + q \hat{j} - 4 \hat{k}$ , then the point $(p, q)$ lies on a line:

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Important Questions on Vector Algebra

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 3rd April 2016>Q 76

Let

\vec{a}, \vec{b}

and

\vec{c}

be three unit vectors such that

\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\sqrt{3}}{2} (\vec{b} + \vec{c}) .

If

\vec{b}

is not parallel to

\vec{c}

, then the angle between

\vec{a}

and

\vec{b}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 10th April 2015>Q 77

Let

\vec{a}

and

\vec{b}

be two unit vectors such that

|\vec{a} + \vec{b}| = \sqrt{3}

. If

\vec{c} = \vec{a} + 2 \vec{b} + (\vec{a} \times \vec{b})

, then

2 |\vec{c}|

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 4th April 2015>Q 78

Let $\vec{a}, \vec{b} and \vec{c}$ be three non - zero vectors such that no two of them are collinear and $(\vec{a} \times \vec{b}) \times \vec{c} = \frac{1}{3} |\vec{b}| |\vec{c}| \vec{a}$ . If $θ$ is the angle between vectors $\vec{b} and \vec{c}$ , then a value of $\sin θ$ is