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

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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

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Important Questions on Vector Algebra

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JEE Advanced

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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

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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

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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?

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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

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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

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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

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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

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 13 - Vector Algebra>Target Exercises>Q 60

If

\vec{a}, \vec{b}, \vec{c}

and

\vec{d}

are the unit vectors such that

(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d}) = 1

and

\vec{a} \cdot \vec{c} = \frac{1}{2},

then