Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 62

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If the position vector of the vertices, $A, B, C$ of a $∆ A B C$ are $7 \hat{j} + 10 \hat{k}, - \hat{i} + 6 \hat{j} + 6 \hat{k}$ and $- 4 \hat{i} + 9 \hat{j} + 6 \hat{k}$ respectively, then triangle is

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Important Questions on Vector Algebra

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Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 63

If

P, Q, R

are respectively the mid point of

A B, A C

and

B C

in

∆ A B C

, then

\vec{B Q} + \vec{A R}

is equal to

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Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 64

The position vectors of the points

A, B, C

are

(2 \hat{i} + \hat{j} - \hat{k}), (3 \hat{i} - 2 \hat{j} + \hat{k})

and

(\hat{i} + 4 \hat{j} - 3 \hat{k})

respectively. These points

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Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 65

Two forces are such that the sum of their magnitudes is

18 N

and the magnitude of their resultant is

12 N

. If the resultant is perpendicular to the smaller forces, then the magnitudes of the forces are –

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Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 66

A girl walks 4 km westward. then she walks 3 km in a direction 30^o East of North and stop. Then, the girl displacement from her initial point of departure, is

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Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 67

(2 \hat{i} - 4 \hat{j}) \cdot (\hat{i} + \hat{j} + \hat{k}) =

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Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 68

(- 3, λ, 1) ⊥ (1, 0, - 3) \Rightarrow λ =

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Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 69

If

\vec{a} \cdot \vec{b} = \vec{c} \cdot \vec{a}

for all vector

\vec{a}

, then

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Achieve CUET (UG) Mathematics Practice Book>Chapter 10 - Vector Algebra>Exercise>Q 70

If

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

, then