Find a vector in the direction of vector 2 i ^ - 3 j ^ + 6 k ^ which has magnitude 21 units.

Let a → = 2 i ^ - 3 j ^ + 6 k ^ To find: A vector of 21 units in the direction of the vector a → . We know that, unit vector along a → is a ^ = a → a → So, a ^ = 2 i ^ - 3 j ^ + 6 k ^ 2 2 + - 3 2 + 6 2 = 2 i ^ - 3 j ^ + 6 k ^ 49 = 2 i ^ - 3 j ^ + 6 k ^ 7 So, vector of 21 units is 21 a ^ = 21 2 i ^ - 3 j ^ + 6 k ^ 7 = 6 i ^ - 9 j ^ + 18 k ^

Find a vector in the direction of vector 2 i ^ - 3 j ^ + 6 k ^ which has magnitude 21 units.

Let a → = 2 i ^ - 3 j ^ + 6 k ^ To find: A vector of 21 units in the direction of the vector a → . We know that, unit vector along a → is a ^ = a → a → So, a ^ = 2 i ^ - 3 j ^ + 6 k ^ 2 2 + - 3 2 + 6 2 = 2 i ^ - 3 j ^ + 6 k ^ 49 = 2 i ^ - 3 j ^ + 6 k ^ 7 So, vector of 21 units is 21 a ^ = 21 2 i ^ - 3 j ^ + 6 k ^ 7 = 6 i ^ - 9 j ^ + 18 k ^

If a → = 4 and - 3 ≤ λ ≤ 2 , then write the range of | λ a ^ | .

Given, a → = 4 It is given that - 3 ≤ λ ≤ 2 ⇒ - 3 × | a → | ≤ λ | a → | ≤ 2 × | a → | ⇒ - 3 × 4 ≤ | λ a → | ≤ 2 × 4 ( k | a → | = | k a → | , k is scalar) ⇒ - 12 ≤ | λ a → | ≤ 8 Thus, the range of | λ a → | is [ - 12 , 8 ] .

In a triangle O A C , if B is the mid-point of side A C and O A → = a → , O B → = b → , then what is O C → ?

In △ O A C , O A → = a → and O B → = b → It is given that B is the mid-point of A C So, B divides A C in the ratio 1 : 1 ∴ Position vector of B = 1 Position vector of A + 1 Position vector of C 1 + 1 ⇒ O B → = O A → + O C → 2 ⇒ b → = a → + O C → 2 ⇒ O C → = 2 b → - a →

E M B I B E

MATHEMATICS CLASS XII VOLUME-2>Chapter 4 - Algebra of Vectors>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 49

EASY

12th CBSE

IMPORTANT

Earn 100

Find a vector in the direction of vector $2 \hat{i} - 3 \hat{j} + 6 \hat{k}$ which has magnitude $21$ units.

Important Questions on Algebra of Vectors

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 4 - Algebra of Vectors>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 50

If

|\vec{a}| = 4

and

- 3 \leq λ \leq 2

, then write the range of

| λ \hat{a} |

.

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 4 - Algebra of Vectors>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 51

In a triangle

O A C

, if

B

is the mid-point of side

A C

and

\vec{O A} = \vec{a}, \vec{O B} = \vec{b}

, then what is

\vec{O C}

?

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 4 - Algebra of Vectors>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 52

Write the position vector of the point which divides the join of points with position vectors

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

and

2 \vec{a} + 3 \vec{b}

in the ratio

2 : 1

.

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 4 - Algebra of Vectors>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 1

If in a $△ A B C$ , $A \equiv (0, 0), B \equiv (3, 3 \sqrt{3}), C \equiv (- 3 \sqrt{3}, 3)$ then the vector of magnitude $2 \sqrt{2}$ units directed along $A O$ , where $O$ is the circumcentre of $△ A B C$ is