Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 20

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If the vectors $\vec{a}, \vec{b}, \vec{c}$ are coplanar, then the value of $|\begin{matrix} \vec{a} & \vec{b} & \vec{c} \\ \vec{a} \cdot \vec{a} & \vec{a} \cdot \vec{b} & \vec{a} \cdot \vec{c} \\ \vec{b} \cdot \vec{a} & \vec{b} \cdot \vec{b} & \vec{b} \cdot \vec{c} \end{matrix}| =$

50% studentsanswered this correctly

Important Questions on Vector Algebra

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 21

If

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

are three non-coplanar, non-zero vectors, then value of

(\vec{a} \cdot \vec{a}) (\vec{b} \times \vec{c}) + (\vec{a} \cdot \vec{b}) (\vec{c} \times \vec{a}) + (\vec{a} \cdot \vec{c}) (\vec{a} \times \vec{b})

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 22

The vectors

\vec{a} \times (\vec{b} \times \vec{c}), \vec{b} \times (\vec{c} \times \vec{a})

and

\vec{c} \times (\vec{a} \times \vec{b})

are

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 23

Given three unit vectors

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

no two of which are collinear satisfying

\vec{a} \times (\vec{b} \times \vec{c}) = \frac{1}{2} \vec{b}

. The angle between

\vec{a}

and

\vec{b}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 24

If

\vec{a}

and

\vec{b}

are unit vectors, then the vector

(\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b})

is parallel to the vector

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 25

The unit vector which is orthogonal to the vector

3 \hat{i} + 2 \hat{j} + 6 \hat{k}

and is coplanar with the vectors

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

and

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

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 26

If

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

are three unit vectors such that

\vec{a} \times (\vec{b} \times \vec{c}) = \frac{1}{2} (\vec{b} + \vec{c})

. If the vectors

\vec{b}

and

\vec{c}

are non-parallel, then the angle between

\vec{a}

and

\vec{b}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.3>Q 27

If

\vec{a}, \vec{c}, \vec{d}

are non-coplanar vectors, then

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

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 31 - Vector Algebra>EXERCISE 11.4>Q 28

If

\vec{A} = 2 \hat{i} + \hat{k}, \vec{B} = \hat{i} + \hat{j} + \hat{k}

and

\vec{C} = 4 \hat{i} - 3 \hat{j} + 7 \hat{k},

then a vector

\vec{r}

which satisfies

\vec{r} \times \vec{B} = \vec{C} \times \vec{B}

and

\vec{r} \cdot \vec{A} = 0,

is