Let a → , b → and c → are non-zero vectors such that they are not orthogonal pairwise and such that V 1 → = a → × b → × c → and V 2 → = ( a → × b → ) × c → , are equal, then which of the following hold(s) good? Note: Question Corrected.

b → = λ a → × c → where λ is a scalar

Let a → , b → and c → are non-zero vectors such that they are not orthogonal pairwise and such that V 1 → = a → × b → × c → and V 2 → = ( a → × b → ) × c → , are equal, then which of the following hold(s) good? Note: Question Corrected.

b → = λ a → × c → where λ is a scalar

Given three vectors U → = 2 i ^ + 3 j ^ – 6 k ^ , V → = 6 i ^ + 2 j ^ + 3 k ^ and W → = 3 i ^ – 6 j ^ – 2 k ^ . Which of the following holds good for the vectors U → , V → and W → ?

U → , V → and W → are linearly dependent.

Let a → , b → , c → be non-zero vectors and | a → | = 1 and r → is a non-zero vector such that r → × a → = b → and r → · c → = 1 , then

r → . a → = 1 – [ a → b → c → ] a → . b →

If a → and b → are two unit vectors perpendicular to each other and c → =λ 1 a → + λ 2 b → + λ 3 ( a → x b → ) , then the following is (are) true

λ 1 + λ 2 + λ 3 = ( a → + b → + a → × b → ). c →

λ 3 = ( a → × b → )× c →

Given three non-coplanar vectors O A → = a → , O B → = b → , O C → = c → . Let S be the centre of the sphere passing through the points O , A , B , C , if O S → = X → , then

X → = a 2 ( b → × c → )+ b 2 ( c → × a → )+ c 2 ( a → × b → ) 2 [ a → b → c → ] , a = a → , b = b → , c = c →

If a → = i ∧ + j ∧ + k ∧ and b → = i ∧ – j ∧ , then the vectors ( a → · i ∧ ) i ∧ + ( a → · j ∧ ) j ∧ + ( a → · k ∧ ) k ∧ ,( b → · i ^ ) i ∧ +( b → · j ∧ ) j ∧ + ( b → · k ∧ ) k ∧ and i ∧ + j ∧ – 2 k ∧

form a parallelepiped of volume 6 units

form a parallelepiped of volume 3 units

If a → = x i ∧ + y j ∧ + z k ∧ , b → = y i + z ∧ j + ∧ x k ∧ , c → = z i ∧ + x j ∧ + y k ∧ , then a → × ( b → × c → ) is

Orthogonal to y + z i ∧ + (z + x) j ∧ + (x + y) k ∧

Parallel to i ∧ + j ∧ + k ∧

HARD

JEE Advanced

IMPORTANT

Earn 100

Let $\vec{a}, \vec{b}$ and $\vec{c}$ are non-zero vectors such that they are not orthogonal pairwise and such that $\vec{V_{1}} = \vec{a} \times (\vec{b} \times \vec{c})$ and $\vec{V_{2}} = (\vec{a} \times \vec{b}) \times \vec{c},$ are equal, then which of the following hold(s) good?

Note: Question Corrected.

50% studentsanswered this correctly

Important Questions on Product of Vectors

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 87

Given three vectors

\vec{U} = 2 \hat{i} + 3 \hat{j} - 6 \hat{k}, \vec{V} = 6 \hat{i} + 2 \hat{j} + 3 \hat{k}

and

\vec{W} = 3 \hat{i} - 6 \hat{j} - 2 \hat{k}

. Which of the following holds good for the vectors

\vec{U}, \vec{V}

and

\vec{W}

?

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 88

Let

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

and

\vec{c} = \hat{i} + \hat{j} - 2 \hat{k}

be three vectors. A vector in the plane of

\vec{b}

and

\vec{c}

whose projection on

\vec{a}

is of magnitude

\sqrt{\frac{2}{3}}

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 89

Three vectors $\vec{a}$ $(|\vec{a}| \neq 0),$ $\vec{b}$ and $\vec{c}$ are such that $\vec{a} \times \vec{b} = 3 \vec{a} \times \vec{c}$ . Also, $|\vec{a}| = |\vec{b}| = 1$ and $|\vec{c}| = \frac{1}{3},$ If the angle between $\vec{b}$ and $\vec{c}$ is $60^{0},$ then

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 90

Let $\vec{a}, \vec{b}, \vec{c}$ be non-zero vectors and $| \vec{a} | = 1$ and $\vec{r}$ is a non-zero vector such that $\vec{r} \times \vec{a} = \vec{b}$ and $\vec{r} \cdot \vec{c} = 1$ , then

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 91

\vec{a}

and

\vec{b}

are two unit vectors perpendicular to each other and

\vec{c} {=λ}_{1} \vec{a} {+ λ}_{2} \vec{b} {+ λ}_{3} (\vec{a} x \vec{b})

, then the following is (are) true

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 92

Given three non-coplanar vectors $\vec{O A} = \vec{a}, \vec{O B} = \vec{b}, \vec{O C} = \vec{c}$ . Let S be the centre of the sphere passing through the points $O, A, B, C$ , if $\vec{O S} = \vec{X}$ , then

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 93

If $\vec{a} = \overset{\land}{i} + \overset{\land}{j} + \overset{\land}{k} and \vec{b} = \overset{\land}{i} – \overset{\land}{j}$ , then the vectors $(\vec{a} · \overset{\land}{i}) \overset{\land}{i} + (\vec{a} · \overset{\land}{j}) \overset{\land}{j} + (\vec{a} · \overset{\land}{k}) \overset{\land}{k},(\vec{b} · \hat{i}) \overset{\land}{i} +(\vec{b} · \overset{\land}{j}) \overset{\land}{j} + (\vec{b} · \overset{\land}{k}) \overset{\land}{k} and \overset{\land}{i} + \overset{\land}{j} – 2 \overset{\land}{k}$

HARD

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 2 - Product of Vectors>Exercise for Session 2>Q 94

\vec{a} = x \overset{\land}{i} + y \overset{\land}{j} + z \overset{\land}{k}, \vec{b} = y \overset{\land}{i + z} \overset{\land}{j +} x \overset{\land}{k}, \vec{c} = z \overset{\land}{i} + x \overset{\land}{j} + y \overset{\land}{k}

, then

\vec{a} × (\vec{b} × \vec{c})

Let a→, b→ and c→ are non-zero vectors such that they are not orthogonal pairwise and such that V1→=a→×b→×c→ and V2→=(a→×b→)×c→, are equal, then which of the following hold(s) good? Note: Question Corrected.

Important Questions on Product of Vectors

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