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

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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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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 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

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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 20

If

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

are coplanar, then

a b c + 2

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 26

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

and

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

then the value of

l + m + n

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 28

If the volume of the parallelepiped with coterminous edges

- p \hat{i} + 5 k, \hat{i} - \hat{j} + q \hat{k}

and

3 \hat{i} - 5 \hat{j}

is

8,

then

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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 29

If the volume of tetrahedron where vertices

(1, 2, 0), (2, 0, 4), (- 1, 2, 0)

and

(- 1, 1, λ)

is

\frac{2}{3}

cu. unit, then find the value of

λ

.