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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be non-coplanar unit vectors equally inclined to one another at an acute angle $θ$ . Then $|[\vec{a} \vec{b} \vec{c}]|$ in terms of $θ$ is equal to

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Important Questions on Vector Algebra

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 12

Let

\vec{r}

be a vector perpendicular to

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

, where

[\vec{a} \vec{b} \vec{c}] = 2

. If

\vec{r} = l (\vec{b} \times \vec{c}) + m (\vec{c} \times \vec{a}) + n (\vec{a} \times \vec{b})

, then

l + m + n

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 13

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

are three non-coplanar non-zero vectors and

\vec{r}

is any vector in space, then

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

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 15

Let $2 \vec{c} + \vec{b} = 4 \vec{a} + 3 \vec{d}$ . If $[\vec{d} \vec{c} \vec{a}]$ and $[\vec{a} \vec{b} \vec{d}]$ are natural numbers with H.C.F. equal to $1$ then how many statement are true among below six statement.

(i) $[\vec{a} \vec{b} \vec{d}] = 2$
(ii) $[\vec{a} \vec{b} \vec{c}] = 3$
(iii) $[\vec{d} \vec{c} \vec{b}] = 4$
(iv) $[\vec{d} \vec{c} \vec{a}] = 1$
(v) $(\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) = 2 \vec{c} - 3 \vec{d}$
(vi) $(\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) = 4 \vec{a} - \vec{b}$

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 16

Let

\vec{u}

and

\vec{v}

are unit vectors and

\vec{w}

is a vector such that

(\vec{u} \times \vec{v}) + \vec{u} = \vec{w}

and

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

then the value of

[\begin{array}{l} \vec{u} & \vec{v} & \vec{w} \end{array}]

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 17

A plane meets the coordinate axes in

A, B, C

and

(α, β, γ)

is the centroid of the triangle

A B C,

then the equation of the plane is

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 22

If the circumcentre of the tetrahedron

O A B C

is given by

\frac{\vec{a^{2}} (\vec{b} \times \vec{c}) + \vec{b^{2}} (\vec{c} \times \vec{a}) + \vec{c^{2}} (\vec{a} \times \vec{b})}{α},

where

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

are the position vectors of the points

A, B, C

respectively relative to the origin

O

such that

[\vec{a,} \vec{b}, \vec{c}] = 36

, then

α

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 24

About the line

\frac{x - 1}{2} = \frac{y - 2}{- 3} = \frac{z + 3}{1}

, the plane

3 x + 4 y + 6 z + 7 = 0

is rotated till the plane passes through the origin. Now,

4 x + α y + β z = 0

is the equation of plane in new position. The value of

α^{2} + β^{2}

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Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-2>Q 26

A vector

\vec{a}

has components

2 p

and

1

with respect to a rectangular cartesian system. The system is rotated through a certain angle about the origin in the counterclockwise sense. If with respect to the new system,

\vec{a}

has components

p + 1

and

1,

then

Let a→, b→ and c→ be non-coplanar unit vectors equally inclined to one another at an acute angle θ. Then a→b→c→ in terms of θ is equal to

Important Questions on Vector Algebra

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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be non-coplanar unit vectors equally inclined to one another at an acute angle $θ$ . Then $|[\vec{a} \vec{b} \vec{c}]|$ in terms of $θ$ is equal to