EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2020 (12-Oct Shift-1)>Q 1

EASY

MHT-CET

IMPORTANT

Earn 100

The value of $m,$ if the vectors $\hat{i} - \hat{j} - 6 \hat{k}, \hat{i} - 3 \hat{j} + 4 \hat{k}$ and $2 \hat{i} - 5 \hat{j} + m \hat{k}$ are coplanar, is

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Important Questions on Vectors

EASY

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2019>Q 2

If the vectors

x \hat{i} - 3 \hat{j} + 7 \hat{k}

and

\hat{i} + y \hat{j} - z \hat{k}

are collinear then the value of

\frac{x y^{2}}{z}

is equal

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2018>Q 3

If planes

\vec{r} . (p \hat{i} - \hat{j} + 2 \hat{k}) + 3 = 0

and

\vec{r} . (2 \hat{i} - p \hat{j} - \hat{k}) - 5 = 0

include angle

\frac{π}{3}

then the value of

p

is

EASY

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2020 (13-Oct Shift 1)>Q 4

If

\vec{A B} = 3 \hat{ı} + 5 \hat{j} + 4 \hat{k}

,

\vec{A C} = 5 \hat{i} - 5 \hat{j} + 2 \hat{k}

represent the sides of a triangle

A B C

, then the length of the median through

A

is

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2017>Q 5

If the origin and the points

P (2, 3, 4), Q (1, 2, 3)

and

R (x, y, z)

are co-planar then

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2018>Q 6

The equation of line passing through

(3, - 1, 2)

and perpendicular to the lines

\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + λ (2 \hat{i} - 2 \hat{j} + \hat{k})

and

\vec{r} = (2 \hat{i} + \hat{j} - 3 \hat{k}) + μ (\hat{i} - 2 \hat{j} + 2 \hat{k})

is

EASY

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2020 (13-Oct Shift 1)>Q 7

If the vectors

\vec{a} = \hat{ı} - 2 \hat{j} + \hat{k}

,

\vec{b} = 2 \hat{ı} - 5 \hat{j} + p \hat{k}

and

\vec{c} = 5 i - 9 \hat{j} + 4 \hat{k}

are coplanar, then the value of

p

is

MEDIUM

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2020 (12-Oct Shift-1)>Q 8

If

\vec{a} = \frac{1}{\sqrt{10}} (3 \hat{ı} + \hat{k}), \vec{b} = \frac{1}{7} (2 \hat{ı} + 3 \hat{ȷ} - 6 \hat{k}),

then the value of

(2 \vec{a} - \vec{b}) \cdot [(\vec{a} \times \vec{b}) \times ((\vec{a} + 2 \vec{b})]

is

MEDIUM

MHT-CET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Vectors>MHT-CET 2020 (12-Oct Shift-1)>Q 9

If

[\begin{array}{ll} \vec{a} & \vec{b} & \vec{c} \end{array}] = 4

, then the volume of the parallelopiped with coterminus edges

\vec{a} + 2 \vec{b}

,

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

is