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QUESTION: 1

If a, b, c and d are the position vectors of the points A, B, C and D such that a + c = b + d, then ABCD is a

Solution:

QUESTION: 2

For what values of x and y, the vectorsare equal?

Solution:

For equal vector

2x=3

and 2x=y

QUESTION: 3

Two or more vectors having the same initial point are called

Solution:
Two or more vectors having the same initial point are called coinitial vector. Two or more vectors are said to be collinear,if they are parallel to the same line,irrespective of their magnitudes and directions.

QUESTION: 4

If ,the vectors a and b are ______ .

Solution:

QUESTION: 5

If the magnitude of the position vector is 7, the value of x is:

Solution:

7 = (x^{2} + 2^{2} + (2x)^{2})^{1/2}

49 = x2 + 2^{2} + 4x^{2}

= 4 + 5x^{2}

5x^{2} = 45

x^{2} = 9

x = ±3

QUESTION: 6

If , then

Solution:

QUESTION: 7

What is the additive identity of a vector?

Solution:

QUESTION: 8

The angles α, β, γ made by the vector with the positive directions of X, Y and Z-axes respectively, then the direction cosines of the vector are:

Solution:

cos α, cos β, cos γ

As per the definition of Direction Cosines.

QUESTION: 9

If a and b are the position vectors of two points A and B and C is a point on AB produced such that AC = 3AB, then position vector of C will be

Solution:

AC = 3AB

(c - a)= 3(b - a). (c - a)

= 3b -3a

c= 3b--2a

QUESTION: 10

Vector of magnitude 1 is called.

Solution:
A vector whose magnitude (i.e., length) is equal to 1 is called a unit vector. There are exactly two unit vectors in any given direction and one is the negative of the other.

QUESTION: 11

If and , then the value of scalars x and y are:

Solution:

a = i + 2j

b = -2i + j

c = 4i +3j

c = xa +yb

4i + 3j = x*(i + 2j) + y*(-2i +j)

= xi + 2xj - 2yi + yj

= (x-2y)i + (2x+y)j

So,

x-2y = 4

2x+y = 3

After solving,

x = 2

y = -1

QUESTION: 12

The direction of zero vector.

Solution:

Zero vector is the unit vector having zero length ,hence the direction is undefined.

QUESTION: 13

The unit vector in the direction of , where A and B are the points (2, – 3, 7) and (1, 3, – 4) is:

Solution:

Point A(2,-3,7)

Point B(1,3,-4)

Let vector in the direction of AB be C.

So,

C=B- A

= (1,3,-4) - (2,-3,7)

= (1-2 , 3+3 , -4-7 )

= (-1,6,-11)

= -1i + 6j -11k

Unit_vector = (Vector)/(Magnitude of vector)

C = (C_vector)/(Magnitude of C_vector) = (-1i + 6j -11k)/158

QUESTION: 14

If a be magnitude of vector then

Solution:

Since a is the magnitude of the vector, it is always positive and it can be 0 in case of zero vectors.

So, a ≥ 0

QUESTION: 15

A vector of magnitude 14 units, which is parallel to the vector

Solution:

Magnitude of i+2j-3k

=√[1^2+2^2+(-3)^2]=√14

= 14(i+2j-3k)/√14

QUESTION: 16

For any two vectors a and b

Solution:

QUESTION: 17

Vectors that may be subject to its parallel displacement without changing its magnitude and direction are called _________.

Solution:

A vector whose point of application is not fixed but magnitude and direction is, is called free vector. They are vectors which you can move anywhere in the plane. Free vectors are those who do not have a specified position in the plane. Also it can be moved parallel to itself.

QUESTION: 18

A vector whose initial and terminal points coincide, is called

Solution:

A vector whose initial and terminal points coincide has no particular direction and 0 magnitude. Therefore, it is called zero vector.

QUESTION: 19

A point from a vector starts is called …… and where it ends is called its ……

Solution:

A vector is a specific quantity drawn as a line segment with an arrowhead at one end. It has an **initial point**, where it begins, and a **terminal point**, where it ends. A vector is defined by its magnitude, or the length of the line, and its direction, indicated by an arrowhead at the terminal point.

QUESTION: 20

If are position vectors of the points (- 1, 1) and (m, – 2). then for what value of m, the vectors are collinear.

Solution:

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