Vectors a -3 -2 -k- b -3 -5 k- and c -2 -4 k- have a characteristics to formA- equilateral triangleB- isosceles triangleC- right angled triangleD- scalene triangle

The correct option is C right angled triangle nbsp;Here, nbsp; b + c = (î 3ĵ + 5k̂) + (2î+ĵ 4k̂) = 3î 2ĵ + k̂ ⇒b + c = a ∴a, b, c represent sides of ...

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Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

Vectors a '=3...

Question

Vectors $\to a = (3^i - 2^j +^k), \to b = (^i - 3^j + 5^k)$ and $\to c = (2^i +^j - 4^k)$ have a characteristics to form

equilateral triangle

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isosceles triangle

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right angled triangle

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scalene triangle

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Solution

The correct option is C right angled triangle

Here,
$\to b + \to c = (^i - 3^j + 5^k) + (2^i +^j - 4^k)$
$= 3^i - 2^j +^k$
$\Rightarrow \to b + \to c = \to a$
$∴ \to a, \to b, \to c$ represent sides of a triangle.

$| \to a | = \sqrt{(3)^{2} + (- 2)^{2} + (1)^{2}}$
$= \sqrt{9 + 4 + 1}$
$= \sqrt{14}$

$| \to b | = \sqrt{(1)^{2} + (- 3)^{2} + (5)^{2}}$
$= \sqrt{1 + 9 + 25}$
$\Rightarrow | \to b | = \sqrt{35}$

$| \to c | = \sqrt{(2)^{2} + (1)^{2} + (- 4)^{2}}$
$= \sqrt{4 + 1 + 16}$
$= \sqrt{21}$

$\Rightarrow (\sqrt{21})^{2} + (\sqrt{14})^{2} = (\sqrt{35})^{2}$
$\Rightarrow 21 + 14 = 35$
$35 = 35$
⟹ $| \to c |^{2} + | \to a |^{2} = | \to b |^{2}$

By the Pythagoras theorem, triangle formed by $\to a, \to b$ and $\to c$ is a right angled triangle

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Vectors →a=(3^i−2^j+^k), →b=(^i−3^j+5^k) and →c=(2^i+^j−4^k) have a characteristics to form

Vectors $\to a = (3^i - 2^j +^k), \to b = (^i - 3^j + 5^k)$ and $\to c = (2^i +^j - 4^k)$ have a characteristics to form