The diagram shows a scalene triangle- ABC- with vectors AB-3- and BC-2b- The point M is the midpoint of AC-Find an expression for the vector AM in terms of - and b-

Let $^a,^b a n d^c$ be three unit vectors such that
$^a \times (^b \times^c) = \frac{\sqrt{3}}{2} (^b +^c) .$ If
$^b$ is not parallel to $^c$ , then the angle between $^a$ and $^b$ is

Q. If

^a

and

^b

are two unit vectors such that

^a + 2^b

and

5^a - 4^b

are perpendicular to each other, then the angle between

^a

and

^b

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The diagram shows a scalene triangle, ABC, with vectors −−→AB=3^a and −−→BC=2^b. The point M is the midpoint of AC.Find an expression for the vector −−→AM in terms of ^a and ^b.

The correct option is D (32^a+^b)First we can find the vector −−→AC −−→AC=−−→AB+−−→BC=3^a+2^b Since, M is the midpoint of AC we know that −−→AM=12−−→AC Thus, −−→AM=12(3^a+2^b)=(32^a+^b)

The diagram shows a scalene triangle, $A B C$ , with vectors $- - \to A B = 3^a$ and $- - \to B C = 2^b$ . The point $M$ is the midpoint of $A C$ .Find an expression for the vector $- - \to A M$ in terms of $^a$ and $^b$ .