If a and b are non-zero and non-collinear vectors- then - a b - - - a b - - - a b k- -k- is equal to

Name: JEE- Grade 12- Mathematics- Vector Algebra- Session 06- D03
Uploaded: 2022-07-04T10:36:42+05:30
Description: Let λ= [ a b î ]î+ [ a b ĵ ]ĵ+ [ a b k̂ ]k̂ ⇒λ. i = nbsp; [ a b î ] =(a×b ).î ∴λ= a×b ...

Let λ= [ a b î ]î+ [ a b ĵ ]ĵ+ [ a b k̂ ]k̂ ⇒λ. i = nbsp; [ a b î ] =(a×b ).î ∴λ= a×b ...

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Byju's Answer

Standard XII

Mathematics

Linear Combination of Vectors

If a and b ar...

Question

If $\to a$ and $\to b$ are non-zero and non-collinear vectors, then $[\to a \to b^i]^i + [\to a \to b^j]^j + [\to a \to b^k]^k$ is equal to

\to a + \to b

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\to a \times \to b

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\to a - \to b

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\to b \times \to a

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Solution

The correct option is B $\to a \times \to b$
Let $\to λ = [\to a \to b^i]^i + [\to a \to b^j]^j + [\to a \to b^k]^k$

$\Rightarrow \to λ . \to i = [\to a \to b^i] = (\to a \times \to b) .^i$
$∴ \to λ = \to a \times \to b$

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Similar questions

Q. If

\to a

and

\to b

are non-zero non-collinear vectors, then

[\to a \to b^i]^i + [\to a \to b^j]^j + [\to a \to b^k]^k

is equal to

Q. For non-zero & non-collinear vectors

p

and

q

, the value of

[^i p q]^i + [^j p q]^j + [^k p q]^k

Q. Assertion :Vector

(^i +^j +^k)

is perpendicular to

(^i - 2^j +^k)

Reason: Two non-zero vectors are perpendicular if their dot product is equal to zero.

Q. If

\to a

is a non-zero vector, then the value of

^i \times (\to a \times^i) +^j \times (\to a \times^j) +^k \times (\to a \times^k)

Q. A non-zero vector

\to a

is parallel to the line of intersection of plane

p_{1}

determined by

^i +^j

and

^i

and plane

P_{2}

determined by vectors

^i -^j

and

^i +^k

, then angle between a and vector

^i - 2^j + 2^k

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Linear Combination of Vectors

Standard XII Mathematics

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If →a and →b are non-zero and non-collinear vectors, then [→a →b ^i]^i+[→a →b ^j]^j+[→a →b ^k]^k is equal to

The correct option is B →a×→bLet →λ=[→a →b ^i]^i+[→a →b ^j]^j+[→a →b ^k]^k ⇒→λ.→i=[→a →b ^i]=(→a×→b).^i ∴→λ=→a×→b

If $\to a$ and $\to b$ are non-zero and non-collinear vectors, then $[\to a \to b^i]^i + [\to a \to b^j]^j + [\to a \to b^k]^k$ is equal to

The correct option is B $\to a \times \to b$
Let $\to λ = [\to a \to b^i]^i + [\to a \to b^j]^j + [\to a \to b^k]^k$

$\Rightarrow \to λ . \to i = [\to a \to b^i] = (\to a \times \to b) .^i$
$∴ \to λ = \to a \times \to b$