Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 25

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Three non-coplanar vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are drawn from a common initial point. The angle between the plane passing through the terminal points of these vectors and the vector $\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}$ is

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Important Questions on Vector Algebra

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 26

If

\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{i} + 3 j + 5 \hat{k}

and

\vec{c} = 7 \hat{i} + 9 \hat{j} + 11 \hat{k}

, then the area of parallelogram having diagonals

\vec{a} + \vec{b}

and

\vec{b} + \vec{c}

is

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 27

Two vectors

\vec{A}

and

\vec{B}

are such that

|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|

. The angle between the two vectors will be

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 28

If

\vec{a}, \vec{b}

and

\vec{c}

are unit vectors such that

\vec{a} + \vec{b} + \vec{c} = 0

, then find the angle between

\vec{a}

and

\vec{b}

.

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 29

If

| \vec{a} | = 3, | \vec{b} | = 2, | \vec{c} | = 1

, then the value of

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

is (given that

\vec{a} + \vec{b} + \vec{c} = 0

)

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 30

If

\vec{a} = \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + \hat{j} - 4 \hat{k}, \vec{c} = - \hat{i} + 2 \hat{j} - \hat{k},

then

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

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 31

[\hat{i} \hat{k} \hat{j}] + [\hat{k} \hat{j} \hat{i}] + [\hat{j} \hat{k} \hat{i}]

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 32

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

is equal to

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 33

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

is equal to