Select the correct option from the given alternatives: Let a, b, c be distinct non-negative numbers. If the vectors aiajckikandcicjbkai^+aj^+ck^,i^+k^ and ci^+cj^+bk^ lie in a plane, then c is - Mathematics and Statistics

Question

Select the correct option from the given alternatives:

Let a, b, c be distinct non-negative numbers. If the vectors $a \hat{i} + a \hat{j} + c \hat{k}, \hat{i} + \hat{k} and c \hat{i} + c \hat{j} + b \hat{k}$ lie in a plane, then c is

Options

the arithmetic mean of a and b
the geometric mean of a and b
the harmonic man of a and b
0

MCQ

Solution

the geometric mean of a and b

shaalaa.com

Vectors and Their Types

Is there an error in this question or solution?

Q I) 18)Q I) 17)Q I) 19)

Chapter 5: Vectors - Miscellaneous exercise 5 [Page 189]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board

Chapter 5 Vectors
Miscellaneous exercise 5 | Q I) 18) | Page 189

RELATED QUESTIONS

If $\vec{a} = x \hat{i} + 2 \hat{j} - z \hat{k} and \vec{b} = 3 \hat{i} - y \hat{j} + \hat{k}$ are two equal vectors ,then write the value of x+y+z

For what value of 'a' the vectors $2 \hat{i} - 3 \hat{j} + 4 \hat{k} and a \hat{i} + 6 \hat{j} - 8 \hat{k}$ are collinear?

If $\vec{a} = x \hat{i} + 2 \hat{j} - z \hat{k} and \vec{b} = 3 \hat{i} - y \hat{j} + \hat{k}$ are two equal vectors, then write the value of x + y + z.

Find the position vector of the mid-point of the vector joining the points

P (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) and Q (4 \hat{i} + \hat{j} - 2 \hat{k}) .

If $\vec{a}$ and $\vec{b}$ are non- collinear vectors, find the value of x such that the vectors $\bar{α} = (x - 2) \vec{a} + \vec{b}$ and $\bar{β} = (3 + 2 x) \bar{a} - 2 \bar{b}$ are collinear.

Find a unit vector perpendicular to each of the vectors $\vec{a} + \vec{b} and \vec{a} - \vec{b} where \vec{a} = 3 \hat{i} + 2 \hat{j} + 2 \hat{k} and \vec{b} = i + 2 \hat{j} - 2 \hat{k}$

In the triangle PQR, $\bar{PQ} = \bar{2a}, \bar{QR} = \bar{2b}$ . The midpoint of PR is M. Find the following vectors in terms of $\bar{a}$ and $\bar{b}$ :

(i) $\bar{PR}$ (ii) $\bar{PM}$ (iii) $\bar{QM}$ .

Select the correct option from the given alternatives:

The volume of tetrahedron whose vectices are (1,-6,10), (-1, -3, 7), (5, -1, λ) and (7, -4, 7) is 11 cu units, then the value of λ is

Select the correct option from the given alternatives:

If l, m, n are direction cosines of a line then $l \hat{i} + m \hat{j} + n \hat{k}$ is ______

Select the correct option from the given alternatives:

If $| \bar{a} | = 3$ and - 1 ≤ k ≤ 2, then $| k \bar{a} |$ lies in the interval

Select the correct option from the given alternatives:

If $\bar{a} and \bar{b}$ are unit vectors, then what is the angle between $\bar{a}$ and $\bar{b}$ for $\sqrt{3} \bar{a} - \bar{b}$ to be a unit vector?

Select the correct option from the given alternatives:

The value of $\hat{i} . (\hat{j} \times \hat{k}) + \hat{j} . (\hat{i} \times \hat{k}) + \hat{k} . (\hat{i} \times \hat{j})$ is

Let $\bar{a} = \hat{i} - \hat{j}, \bar{b} = \hat{j} - \hat{k}, \bar{c} = \hat{k} - \hat{i} .$ If $\bar{d}$ is a unit vector such that $\bar{a} \cdot \bar{d} = 0 = [\begin{matrix} \bar{b} & \bar{c} & \bar{d} \end{matrix}]$ , then $\bar{d}$ equals ______.

In a parallelogram ABCD, diagonal vectors are $\bar{AC} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k} and \bar{BD} = - 6 \hat{i} + 7 \hat{j} - 2 \hat{k}$ , then find the adjacent side vectors $\bar{AB} and \bar{AD}$ .

Find the component form of $\bar{a}$ if it lies in YZ-plane makes 60° with positive Y-axis and $| \bar{a} | = 4$ .

If ABC is a triangle whose orthocentre is P and the circumcentre is Q, prove that $\bar{PA} + \bar{PB} + \bar{PC} = 2 \bar{PQ} .$

If P is orthocentre, Q is the circumcentre and G is the centroid of a triangle ABC, then prove that $\bar{QP} = 3 \bar{QG}$ .

Dot product of a vector with vectors $3 \hat{i} - 5 \hat{k}, 2 \hat{i} + 7 \hat{j} and \hat{i} + \hat{j} + \hat{k}$ are respectively -1, 6 and 5. Find the vector.

Express $\hat{i} + 4 \hat{j} - 4 \hat{k}$ as the linear combination of the vectors $2 \hat{i} - \hat{j} + 3 \hat{k}, \hat{i} - 2 \hat{j} + 4 \hat{k}$ and $- \hat{i} + 3 \hat{j} - 5 \hat{k}$ .

Let bar"b" = 4hat"i" + 3hat"j" and bar"c" be two vectors perpendicular to each other in the XY-plane. Find the vector in the same plane having projection 1 and 2 along bar"b" and bar"c" respectively.

For any non-zero vectors a and b, [b a × b a] = ?

For any vector $\bar{x}$ the value of ${(\bar{x} \times \hat{i})}^{2} + {(\bar{x} \times \hat{j})}^{2} + {(\bar{x} \times \hat{k})}^{2}$ is equal to ______

If A, B, C and D are (3, 7, 4), (5, -2, - 3), (- 4, 5, 6) and(1, 2, 3) respectively, then the volume of the parallelopiped with AB, AC and AD as the co-terminus edges, is ______ cubic units.

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 $\frac{{xy}^{2}}{z}$ is equal.

Find a vector of magnitude 11 in the direction opposite to that of $\vec{PQ}$ where P and Q are the points (1, 3, 2) and (–1, 0, 8), respectively.

The angle between the vectors $\hat{i} - \hat{j}$ and $\hat{j} - \hat{k}$ is ______.

If $\vec{a}$ and $\vec{b}$ are unit vectors, then what is the angle between $\vec{a}$ and $\vec{b}$ for $\sqrt{3} \vec{a} - \vec{b}$ to be a unit vector?

Find the unit vector in the direction of the sum of the vectors $\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}$ and $\vec{b} = 2 \hat{j} + \hat{k}$ .

If $\vec{a} = \hat{i} + \hat{j} + 2 \hat{k}$ and $\hat{b} = 2 \hat{i} + \hat{j} - 2 \hat{k}$ , find the unit vector in the direction of $2 \vec{a} - \vec{b}$

Classify the following as scalar and vector quantity.

Velocity

In Figure, identify the following vector.

Equal

$\bar{a}, \bar{b}$ and $\bar{c}$ are three vectors such that $\vec{a} + \vec{b} + \vec{c}$ 20, $| \bar{a} | = 1, | \bar{b} | = 2$ and $| \bar{c} | = 3$ . Then $\bar{a} . \bar{b} + \bar{b} . \bar{c} + \bar{c . a}$ is equal to

Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three vectors, then $\bar{a} \times (\bar{b} \times \bar{c}) = (\bar{a} \times \bar{b}) \times \bar{c}$ if

If $\vec{a}$ and $\vec{b}$ are two collinear vectors then which of the following are incorrect.

Find $| \vec{a} \times \vec{b} |$ , if $\vec{a} = \hat{i} - 7 \hat{j} + 7 \hat{k}$ and $\vec{b} = 3 \hat{i} - 2 \hat{j} + 2 \hat{k}$

If points P(4, 5, x), Q(3, y, 4) and R(5, 8, 0) are collinear, then the value of x + y is ______.

Check whether the vectors $2 \hat{i} + 2 \hat{j} + 3 \hat{k}, - 3 \hat{i} + 3 \hat{j} + 2 \hat{k} and 3 \hat{i} + 4 \hat{k}$ form a triangle or not.

lf ΔABC is an equilateral triangle and length of each side is “a” units, then the value of $\bar{A B} \cdot \bar{B C} + \bar{B C} \cdot \bar{C A} + \bar{C A} \cdot \bar{A B}$ is ______.

In the triangle PQR, $\bar{P Q}$ = 2 $\bar{a}$ and $\bar{Q R}$ = 2 $\bar{b}$ . The midpoint of PR is M. Find the following vectors in terms of $\bar{a}$ and $\bar{b}$ .

(i) $\bar{P R}$ (ii) $\bar{P M}$ (iii) $\bar{Q M}$

Select the correct option from the given alternatives: Let a, b, c be distinct non-negative numbers. If the vectors aiajckikandcicjbkai^+aj^+ck^,i^+k^ and ci^+cj^+bk^ lie in a plane, then c is - Mathematics and Statistics

Advertisements

Advertisements

Question

Options

Solution

APPEARS IN

RELATED QUESTIONS

Select a course

Select the correct option from the given alternatives: Let a, b, c be distinct non-negative numbers. If the vectors aiajckikandcicjbkai^+aj^+ck^,i^+k^ and ci^+cj^+bk^ lie in a plane, then c is - Mathematics and Statistics

Advertisements

Advertisements

Question

Options

SolutionShow Solution

APPEARS IN

RELATED QUESTIONS

Select a course

Solution