The magnitude of the projection of 2 -3 -4 k- on the vector -k- will beA- -3B- None of the above C- -3-2D- 3 -3

The correct option is D Let a⃗ and b⃗ be the two vectors as shown The projection of b⃗ along a⃗ will be OA= | b⃗ |cos θ = | b⃗ | ( a⃗.b⃗/ | a⃗ | | ...

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Byju's Answer

Standard IX

Mathematics

Dot Product of Two Vectors

The magnitude...

Question

$T h e m a g n i t u d e o f t h e p r o j e c t i o n o f 2^i + 3^j + 4^k o n t h e v e c t o r^i +^j +^k w i l l b e - --- -$

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None of the above

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Solution

The correct option is C

$L e t \to a a n d \to b b e t h e t w o v e c t o r s a s s h o w n$

$T h e p r o j e c t i o n o f \to b a l o n g \to a w i l l b e O A = ∣ ∣ \to b ∣ ∣ c o s θ = ∣ ∣ \to b ∣ ∣ (\frac{\to a . \to b}{| \to a | ∣ ∣ \to b ∣ ∣}) (c o s θ = \frac{\to a . \to b}{| \to a | ∣ ∣ \to b ∣ ∣}) = \frac{\to a . \to b}{| \to a |} S o m a g n i t u d e o f p r o j e c t i o n o f 2^i + 3^j + 4^k o n^i +^j +^k w i l l b e (2^i + 3^j + 4^k) . \frac{^i +^j +^k}{\sqrt{3}} = \frac{2}{\sqrt{3}} + \frac{3}{\sqrt{3}} + \frac{4}{\sqrt{3}} = \frac{9}{\sqrt{3}} = 3 \sqrt{3} u n i t s$

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Similar questions

$T h e m a g n i t u d e o f t h e p r o j e c t i o n o f 2^i + 3^j + 4^k o n t h e v e c t o r^i +^j +^k w i l l b e - --- -$

Q. The magnitude of the projection of the vector

2^i + 3^j +^k

on the vector perpendicular to the plane containing the vectors

^i +^j +^k

and

^i + 2^j + 3^k,

is:

Q. If

\to A = 2^i + 3^j -^k

and

\to B = -^i + 3^j + 4^k

, then projection of

\to A

\to B

will be

Q. Let,

\to a =^i + 2^j +^k, \to b =^i -^j +^k, \to c =^i +^j -^k .

A vector coplanar to

\to a

and

\to b

has a projection along

\to c

of magnitude

\frac{1}{\sqrt{3}}

, then the vector is

Q. The magnitude of the projection of the vector

2^i + 3^j +^k

on the vector perpendicular to the plane containing the vectors

^i +^j +^k

and

^i + 2^j + 3^k,

is:

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The magnitude of the projection of 2^i+3^j+4^k on the vector ^i+^j+^k will be –––––

$T h e m a g n i t u d e o f t h e p r o j e c t i o n o f 2^i + 3^j + 4^k o n t h e v e c t o r^i +^j +^k w i l l b e - --- -$