Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 51

HARD

JEE Advanced

IMPORTANT

Earn 100

If $\vec{a} = - \hat{i} + \hat{j} + \hat{k}$ and $\vec{b} = 2 \hat{i} + 0 \hat{j} + \hat{k},$ then the vectors $\vec{c}$ satisfying the conditions, that it is coplanar with $\vec{a}$ and $\vec{b}$ , that it is perpendicular to $\vec{b}$ and that $\vec{a} \cdot \vec{c} = 7$ , is

50% studentsanswered this correctly

Important Questions on Vector Algebra

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 52

Let the unit vectors

\hat{a}

and

\hat{b}

be perpendicular to each other and the unit vector

\hat{c}

be inclined at an angle

θ

to both

\hat{a}

and

\hat{b}

. If

\hat{c} = x \hat{a} + y \hat{b} + z (\hat{a} \times \hat{b})

, then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 53

If

\hat{r} \cdot \vec{a} = \hat{r} \cdot \vec{b} = \hat{r} \cdot \vec{c} = 0,

where

\vec{a}, \vec{b}

and

\vec{c}

are non-coplanar, then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 54

If

\vec{a}, \vec{b}

and

\vec{c}

are linearly independent vectors and

Δ = |\begin{matrix} \vec{a} & \vec{b} & \vec{c} \\ \vec{a} \cdot \vec{a} & \vec{a} \cdot \vec{b} & \vec{a} \cdot \vec{c} \\ \vec{a} \cdot \vec{c} & \vec{b} \cdot \vec{c} & \vec{c} \cdot \vec{c} \end{matrix}|,

then

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 55

If vector

\vec{a}

lies in the plane of

\vec{b}

and

\vec{c}

, then which of the following is correct?

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 56

The value of

[\vec{a} - \vec{b} \vec{b} - \vec{c} \vec{c} - \vec{a}],

where

|\vec{a}| = 1

,

|\vec{b}| = 5

and

|\vec{c}| = 3,

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 57

If

\vec{a} = 2 \hat{i} + 3 \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + p \hat{j} + 3 \hat{k}

and

\vec{c} = 2 \hat{i} + 17 \hat{j} - 3 \hat{k}

are coplanar vectors, then the value of

p

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 58

If

\vec{a}, \vec{b}

and

\vec{c}

are three non-coplanar mutually perpendicular unit vectors, then

[\vec{a} \vec{b} \vec{c}]

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 59

For three vectors

\vec{a}, \vec{b}

and

\vec{c}

,

(\vec{a} - \vec{b}) \cdot [(\vec{b} - \vec{c}) \times (\vec{c} - \vec{a})]

equals