MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 8

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If the points $A, B, C$ and $D$ have position vectors $\vec{a}, 2 \vec{a} + \vec{b}, 4 \vec{a} + 2 \vec{b}$ and $5 \vec{a} + 4 \vec{b}$ , respectively, then three collinear points are

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Important Questions on Vectors

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 9

If

\vec{a} = 2 \vec{p} + 3 \vec{q} - \vec{r}, \vec{b} = \vec{p} - 2 \vec{q} + 2 \vec{r}

and

\vec{c} = - 2 \vec{p} + \vec{q} - 2 \vec{r}

and

\vec{R} = 3 \vec{p} - \vec{q} + 2 \vec{r},

where

p, q, r

are non-coplanar vectors, then

\vec{R}

in terms of

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

is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 11

A

and

B

are two points. The position vector of

A

is

6 \vec{b} - 2 \vec{a}

. A point

P

divides the line

A B

in the ratio

1 : 2

. If

\vec{a} - \vec{b}

is the position vector of

P, B

is given by

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 12

\vec{a}, \vec{b}

and

\vec{c}

are position vectors of points

A, B

and

C

, respectively. If

2 \vec{a} + 3 \vec{b} - 5 \vec{c} = 0

then the ratio in which point

C

divides segment

A B

is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 13

If

\vec{O A} = \hat{i} + 3 \hat{j} - 2 \hat{k}

and

\vec{O B} = 3 \hat{i} + \hat{j} - 2 \hat{k}

, then vector

\vec{O C}

bisecting the

∠ A O B

is equal to

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 15

If

2 \vec{a} + \vec{b} = 3 \vec{c},

then

A

divides

B C

in the ratio

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 17

Let

\vec{a} = \hat{i} - \hat{k}, \vec{b} = x \hat{i} + \hat{j} + (1 - x) \hat{k}

and

\vec{c} = y \hat{i} + x \hat{j} + (1 + x - y) \hat{k}

then

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

depends on:

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 18

If the points

(1, 1, 2), (2, 1, p), (1, 0, 3)

and

(2, 2, 0)

are co-planar, then value of

p

is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 13 - Vectors>Critical Thinking>Q 19

If the points

A, B, C

and

D

with position vectors

\hat{i} + \hat{j} + \hat{k}, 2 \hat{i} + 3 \hat{j} + \hat{k}, \hat{i} + 2 \hat{j} + 5 \hat{k}

and

λ \hat{i} + 3 \hat{j} + 4 \hat{k}

are coplanar then

λ

is equal to