Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 43

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Let $\vec{a}, \vec{b}, \vec{c}$ are three vectors along the adjacent edges of a tetrahedron, if $| a | = | b | = | c | = 2$ and $\vec{a} . \vec{b} = \vec{b} . \vec{c} = \vec{c} . \vec{a} = 2$ , then volume of tetrahedron 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 44

Given that, the vectors

\vec{α}

and

\vec{β}

are non-collinear. The values of

x

and

y

for which

\vec{u} - \vec{v} = \vec{w}

holds true, if

\vec{u} = 2 x \vec{α} + y \vec{β}, \vec{v} = 2 y \vec{α} + 3 x \vec{β}

and

\vec{w} = 2 α - 5 β

are

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 45

If

\vec{p}

and

\vec{q}

are non-collinear, non-zero vectors and

(b - c) \vec{p} \times \vec{q} + (c - a) \vec{p} + (a - b) \vec{q} = \vec{0}

where

a, b, c

are the lengths of the sides of a triangle, then triangle is

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 1>Q 46

Three vectors

\vec{a}, \vec{b}

and

\vec{c}

are such that

|\vec{a}| = 1, |\vec{b}| = 2, |\vec{c}| = 4

and

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

. Then, the value of

4 \vec{a} \cdot \vec{b} + 3 \vec{b} \cdot \vec{c} + 3 \vec{c} \cdot \vec{a}

is equal to

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 1

If

P, Q, R

are the mid-points of the sides

\vec{A B}, \vec{B C}, \vec{C A}

, respectively of a

Δ A B C

and

\vec{a}, \vec{p}, \vec{q}

are the position vector of

A, P, Q

, respectively, then what is the position vector of

R

?

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 2

If

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

are non-coplanar vectors and

λ

is a real number, then the vectors

\vec{a} + 2 \vec{b} + 3 \vec{c}, λ \vec{b} + 4 \vec{c}

and

(2 λ - 1) \vec{c}

are non-coplanar for

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 3

In a

Δ A B C, D, E, F

are the mid-points of the sides

B C, C A

and

A B

, respectively, the vector

\vec{A D}

is equal to

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 4

If

D, E

and

F

are respectively mid-points of

A B, A C

and

B C

in

∆ A B C

, then

\vec{B E} + \vec{A F}

is equal to

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Mathematics Crash Course JEE Main>Chapter 32 - Vector Algebra>Level 2>Q 5

Let

O

be the origin. Let

\vec{O P} = x \hat{i} + y \hat{j} - \hat{k}

and

\vec{O Q} = - \hat{i} + 2 \hat{j} + 3 x \hat{k}, x, y \in R, x > 0,

be such that

| \vec{P Q} | = \sqrt{20}

and the vector

\vec{O P}

is perpendicular to

\vec{O Q} .

If

\vec{O R} = 3 \hat{i} + z \hat{j} - 7 \hat{k}, z \in R,

is coplanar with

\vec{O P}

and

\vec{O Q},

then the value of

x^{2} + y^{2} + z^{2}

is equal to