Solution:
(a)
Given: a(3,m) and b (2,-1)
Using dot product formula of vectors:
a.b=∣a∣∣b∣cosθ
⇒3(2)+m(−1)=32+m2×22+(−1)2×cos(360°)⇒6−m=(9+m2)5×(1)⇒(6−m)2=5(9+m2)⇒36+m2−12m=45+5m2⇒4m2+12m+9=0⇒4m2+6m+6m+9=0⇒(4m+3)(2m+3)=0⇒m=−43,−23
(b)
Two sides are :p=(√2+1)cm and b=(√2-1) cm
We need to find the Hypotenuse (h).
Using Pythagoras theorem,
h2=p2+b2
⇒h2=(2+1)2+(2−1)2⇒h2=2+1+22+2+1−22⇒h2=6⇒h=6 cm
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