The three vectors A-3-2-k- B-3-5k- and C-2-4k- form

A⃗=3î 2ĵ+k̂, B⃗=î 3ĵ+5k̂, C⃗=2î ĵ+4k̂ |A⃗|=√(3^2+( 2)^2+1^2)=√(9+4+1)=√(14) |B⃗|=√(1^2+( 3)^2+5^2)=√(1+9+24)=√(35) |A⃗|=√(2^2+1^2+( 4)^2)=√(4+1+16)=√(21) As ...

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Byju's Answer

Standard XI

Physics

Addition and Subtraction in Unit Vector Notation

The three vec...

Question

The three vectors $\to A = 3^i - 2^j +^k, \to B =^i - 3^j + 5^k$ and $\to C = 2^i +^j - 4^k$ form

An equilateral triangle

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Isosceles triangle

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A right angled triangle

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No triangle

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Solution

The correct option is C
A right angled triangle

$\to A = 3^i - 2^j +^k, \to B =^i - 3^j + 5^k, \to C = 2^i -^j + 4^k | \to A | = \sqrt{3^{2} + (- 2)^{2} + 1^{2}} = \sqrt{9 + 4 + 1} = \sqrt{14} | \to B | = \sqrt{1^{2} + (- 3)^{2} + 5^{2}} = \sqrt{1 + 9 + 24} = \sqrt{35} | \to A | = \sqrt{2^{2} + 1^{2} + (- 4)^{2}} = \sqrt{4 + 1 + 16} = \sqrt{21}$
As $B = \sqrt{A^{2} + C^{2}}$ therefore ABC will be right angled triangle.

Suggest Corrections

Similar questions

Q. If

\to a = 2^i +^j + 3^k

\to b = 3^i + 2^j +^k

\to c =^i -^j - 4^k

\to d =^i + 2^j -^k

, then

(\to a \times \to b) \times (\to c \times \to d) =

Q. Show that the vectors

\to a = 3^i - 2^j +^k, \to b =^i - 3^j + 5^k a n d \to c = 2^i +^j - 4^k

form a right angled triangle.

Q. If

\to a =^i + 2^j + 4^k, \to b = 2^i - 3^j +^k

\to c =^i + 4^j - 4^k

then the vector

\to a \times (\to b \times \to c)

is orthogonal to

Q. If

\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k, \to b =^i + 3^j - 2^k

and

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

such that

\to r = l \to a + m \to b + n \to c

, then

Q. Let

\to a =^i +^j +^k

\to b =^i -^j +^k

and

\to c =^i -^j -^k

be three vectors. A vector

\to v

in the plane of

\to a

and

\to b

, whose projection on

\to c

\frac{2}{\sqrt{3}}

, is given by

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The three vectors →A=3^i−2^j+^k,→B=^i−3^j+5^k and →C=2^i+^j−4^k form

The correct option is C A right angled triangle →A=3^i−2^j+^k,→B=^i−3^j+5^k,→C=2^i−^j+4^k|→A|=√32+(−2)2+12=√9+4+1=√14|→B|=√12+(−3)2+52=√1+9+24=√35|→A|=√22+12+(−4)2=√4+1+16=√21 As B=√A2+C2 therefore ABC will be right angled triangle.

The three vectors $\to A = 3^i - 2^j +^k, \to B =^i - 3^j + 5^k$ and $\to C = 2^i +^j - 4^k$ form