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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

isosceles triangle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

right angled triangle

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

scalene triangle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Suggest Corrections

Similar questions

Q. 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

Q. Show that the vectors

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

and

c = 2^i +^j - 4^k

from a right angled triangle.

Q. The vectors

3^i - 2^j +^k,^i - 3^j + 5^k

and

2^i +^j - 4^k

form the sides of a triangle, then triangle is

Q. Show that the vectors

2^i -^j +^k,^i - 3^j - 5^k, 3^i - 4^j - 4^k

form the vertices of a right angled triangle.

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.

Join BYJU'S Learning Program

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