The three vectors A -3 -2 -k- B -3 -5 k- and C -2 -4 k- formA- an equilateral triangleB- isosceles triangleC- a right angled triangleD- no triangle

The correct option is C a right angled triangleA=3î 2ĵ+k̂, B=î 3ĵ+5k̂, C=2î+ĵ 4k̂ | A |=√(3^2+( 2)^2+1^2)=√(9+4+1)=√(14) | B |=√(1^2+( 3)^2+5^2)=√(1+9+25)=√(35 ...

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Byju's Answer

Standard XII

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
$\to A = 3^i - 2^j +^k, \to B =^i - 3^j + 5^k, \to C = 2^i +^j - 4^k$
$∣ ∣ ∣ \to A ∣ ∣ ∣ = \sqrt{3^{2} + (- 2)^{2} + 1^{2}} = \sqrt{9 + 4 + 1} = \sqrt{14}$
$∣ ∣ ∣ \to B ∣ ∣ ∣ = \sqrt{1^{2} + (- 3)^{2} + 5^{2}} = \sqrt{1 + 9 + 25} = \sqrt{35}$
$∣ ∣ ∣ \to A ∣ ∣ ∣ = \sqrt{2^{2} + 1^{2} + (- 4)^{2}} = \sqrt{4 + 1 + 16} = \sqrt{21}$
As $B = \sqrt{A^{2} + C^{2}}$ , therefore $A B C$ will be a right angled triangle.

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Similar questions

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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 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