Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 15

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If the unit vectors $\vec{a}$ and $\vec{b}$ are inclined at an angle $2 θ$ such that $|\vec{a} - \vec{b}| < 1$ and $0 \leq θ \leq π,$ then $θ$ lies in the interval

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Important Questions on Vector Algebra

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 16

If

{\vec{e}}_{1} = (1, 1, 1), {\vec{e}}_{2} = (1, 1, - 1)

and

\vec{a}, \vec{b}

are two vectors such that

{\vec{e}}_{1} = 2 \vec{a} + \vec{b}

and

{\vec{e}}_{2} = \vec{a} + 2 \vec{b},

then angle between

\vec{a}

and

\vec{b}

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 17

If the vector

- \hat{i} + \hat{j} - \hat{k}

bisects the angle between the vector

\vec{c}

and the vector

3 \hat{i} + 4 \hat{j}

, then the unit vector in the direction of

\vec{c}

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 18

If

\hat{a}

and

\hat{b}

are unit vectors such that the vector

\hat{a} + 3 \hat{b}

is perpendicular to

7 \hat{a} - 5 \hat{b}

and

\hat{a} - 4 \hat{b}

is perpendicular to

7 \hat{a} - 2 \hat{b},

then the angle between

\hat{a}

and

\hat{b}

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 19

If

4 \hat{i} + 7 \hat{j} + 8 \hat{k}, 2 \hat{i} + 3 \hat{j} + 4 \hat{k}

and

2 \hat{i} + 5 \hat{j} + 7 \hat{k}

are the position vectors of the vertices

A, B

and

C

, respectively of

Δ A B C

. The position vector of the point where the bisector of angle

A

meets

B C

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 20

If

θ

is the angle between vectors

\vec{a}

and

\vec{b}

such that

\vec{a} \cdot \vec{b} \geq 0,

then

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 21

If

|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|,

then

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 22

If

|\vec{a}| = |\vec{b}| = |\vec{a} + \vec{b}| = 1,

then

|\vec{a} - \vec{b}|

is equal to

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 23

If

\vec{a}, \vec{b}

and

\vec{c}

are three mutually perpendicular vectors of equal magnitude, then the angle

θ

which

\vec{a} + \vec{b} + \vec{c}

makes with anyone of three given vectors is given by