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

SAS Similarity

If a, b a...

Question

If $a$ , $b$ are the vectors forming consecutive sides of a regular hexagon $A B C D E F$ , find the correct option?

\to C E = 2 b - a

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

\to C E = b - 2 a

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

\to A E = 2 b - a

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

\to A E = b - 2 a

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

Open in App

Solution

The correct option is C $\to C E = b - 2 a$
$\to A B = a, \to B C = b$
$∴ \to A C = \to A B + \to B C = a + b$ ...(1)
$\to A D = 2 \to B C = 2 b$ ...(2)
( $∵$ AD is parallel to BC and twice its length).
$\to C D = \to A D - \to A C = 2 b - (a + b) = b - a$ ...(3)
$\to F A = - \to C D = a - b$ ...(4)
$\to D E = - \to A B = - a$ ...(5)
$\to E F = - \to B C = - b$ ...(6)
$\to A E = \to A D + \to D E = 2 b - a$ by (2) and (5) ...(7)
$\to C E = \to C D + \to D E = b - a - a = b - 2 a,$ by (3) and (5) or
$\to C E = \to A E - \to A C = 2 b - a - (a + b) = b - 2 a$ by (1) and (7)

Suggest Corrections

Similar questions

\vec{a}, \vec{b}

\vec{a} + \vec{b}

\vec{a} - \vec{b}

\vec{b} - \vec{a}

- (\vec{a} + \vec{b})

A B C D E F

\to A B - -- - + \to A C - -- - + \to A E - -- - + \to A F - -- - = 2 \to A D - -- - .

A B C D E F

\to A B + \to A C + \to A D + \to A E + \to A F = λ \to A D

λ =

\vec{B}

\vec{C}

\vec{b} and \vec{C D} = \vec{c}

\vec{A E}

\vec{a} + \vec{b} + \vec{c}

2 \vec{a} + \vec{b} + \vec{c}

\vec{b} + \vec{c}

\vec{a} + 2 \vec{b} + 2 \vec{c}

A B C D E F

\to A B + \to A C + \to A D + \to A E + \to A F = k \to A D

k

Join BYJU'S Learning Program