Question

if vectors A = i^ +2j^ +4k^ and B = 5i^ represents the two sides of a triangle , them the third side of the triangle can have length equal to.....

Answer 1

A=i+2j+4k
B=5i
By triangle law of vectors
C=A+B
C=6i+2j+4k
C=2 (3i+j+2k)
lCl=
$2 \sqrt{ {3}^{2} + {1}^{2} + {2}^{2} }$
ICI=
$2 \sqrt{14}$
hope it helps

Answer 2

Answer: The correct answer is $2\sqrt{14 }$.

Explanation:

Use the triangle's law to find the third vector of the triangle from the given two sides of the triangle.

C=A+B

Put A= i+2j+4k and B= 5i in the above expression.

C= ( i+2j+4k)+5i

C= 6i+2j+4k

Find the magnitude of the vector C.

$C=\sqrt{x^{2}+y^{2}+z^{2} }$

Put x=6, y=2 and z=4.

$C=\sqrt{6^{2}+2^{2}+4^{2} }$

$C=2\sqrt{14 }$

Therefore, the third side of the triangle is $2\sqrt{14 }$.