Consider the following inequalities in respect of vectors a and b -1- -a-b- -a-b-2- -a-b- -a-b-Which of the above is-are correct-

The correct option is B Both 1 and 2Solution:1. |a⃗+b⃗|≤|a⃗|+|b⃗| [by triangle inequality]2. #160; |a⃗ b⃗|≥|a⃗| |b⃗| [by reverse triangle inequality ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Linear Combination of Vectors

Consider the ...

Question

Consider the following inequalities in respect of vectors $\to a$ and $\to b$ :
1. $| \to a + \to b | \leq | \to a | + | \to b |$
2. $| \to a - \to b | \geq | \to a | - | \to b |$
Which of the above is/are correct?

1 only

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 only

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Both 1 and 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Neither 1 nor 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B Both 1 and 2
Solution:
1. $| \to a + \to b | \leq | \to a | + | \to b |$
[by triangle inequality]
2. $| \to a - \to b | \geq | \to a | - | \to b |$
[by reverse triangle inequality]
Hence, Both are correct.
Hence, C is the correct option.

Suggest Corrections

Similar questions

Q. Consider the following in respect of two non-singular matrices

A

and

B

of same order:

1. d e t (A + B) = d e t A + d e t B

2. (A + B)^{- 1} = A^{- 1} + B^{- 1}

Which of the above is/are correct?

Q. Consider the following:
1.

A \cup (B \cap C) = (A \cap B) \cup (A \cap C)

A \cap (B \cup C) = (A \cup B) \cap (A \cup C)

Which of the above is/are correct?

Q. Let

G

be an arbitrary group. Consider the following relations on

G

R_{1}

\forall a, b ϵ G, a R_{1} b

if and only if

\exists g ϵ G

such that

a = g^{- 1} b g

R_{2}

\forall a, b ϵ G, a R_{2} b

if and only if

a = b^{- 1}

Which of the above is/are equivalence relation/relations?

Show that (1+|a|^2) (1+|b|^2)=|1-a.b|^2+|a+b+a×b|^2 . For any 2 vectors a and b

Q. Consider the following in respect of two events

A

and

B

:
(1)

P (A

occurs but not

B) = P (A) - P (B)

B \subset A

(2)

P (A

alone or

B

alone occurs)

= P (A) + P (B) - P (A \cap B)

(3)

P (A \cup B) = P (A) + P (B)

A

and

B

are mutually exclusive
Which of the above is/are correct?

Join BYJU'S Learning Program

Consider the following inequalities in respect of vectors →a and →b :1. |→a+→b|≤|→a|+|→b|2. |→a−→b|≥|→a|−|→b|Which of the above is/are correct?

The correct option is B Both 1 and 2Solution:1. |→a+→b|≤|→a|+|→b|[by triangle inequality]2. |→a−→b|≥|→a|−|→b|[by reverse triangle inequality]Hence, Both are correct.Hence, C is the correct option.

Consider the following inequalities in respect of vectors $\to a$ and $\to b$ :
1. $| \to a + \to b | \leq | \to a | + | \to b |$
2. $| \to a - \to b | \geq | \to a | - | \to b |$
Which of the above is/are correct?

The correct option is B Both 1 and 2
Solution:
1. $| \to a + \to b | \leq | \to a | + | \to b |$
[by triangle inequality]
2. $| \to a - \to b | \geq | \to a | - | \to b |$
[by reverse triangle inequality]
Hence, Both are correct.
Hence, C is the correct option.