Câu 1:
\(\overrightarrow{a}=\left(2;5\right);\overrightarrow{b}=\left(-3;1\right)\)
=>\(\overrightarrow{a}\cdot\overrightarrow{b}=2\cdot\left(-3\right)+5\cdot1=-6+5=-1\)
=>Chọn D
Câu 2:
\(A\left(0;3\right);B\left(4;0\right);C\left(-2;-5\right)\)
\(\overrightarrow{AB}=\left(4;-3\right);\overrightarrow{BC}=\left(-6;-5\right)\)
\(\overrightarrow{AB}\cdot\overrightarrow{BC}=4\cdot\left(-6\right)+\left(-3\right)\cdot\left(-5\right)=-24+15=-9\)
=>Chọn D
Câu 3:
\(\overrightarrow{u}=\overrightarrow{i}+3\overrightarrow{j}=\left(1;3\right);\overrightarrow{v}=-2\overrightarrow{i}+2\overrightarrow{j}=\left(-2;2\right)\)
\(\overrightarrow{u}\cdot\overrightarrow{v}=1\cdot\left(-2\right)+3\cdot2=-2+6=4\)
=>Chọn B
Câu 4:
\(\overrightarrow{AB}\cdot\overrightarrow{AC}=AB\cdot AC\cdot cos\left(\overrightarrow{AB};\overrightarrow{AC}\right)\)
\(=AB\cdot AC\cdot cosBAC\)
\(=4a\cdot4a\cdot cos60=16a^2\cdot\dfrac{1}{2}=8a^2\)
=>Chọn A
Câu 5:
\(\overrightarrow{AB}\cdot\overrightarrow{AD}=AB\cdot AD\cdot cos\left(\overrightarrow{AB};\overrightarrow{AD}\right)\)
\(=a\cdot a\cdot cos90=0\)
=>Chọn A
Câu 6:
\(\overrightarrow{a}\cdot\overrightarrow{b}=2\cdot3+5\cdot\left(-7\right)=6-35=-29\)
\(\overrightarrow{a}=\left(2;5\right);\overrightarrow{b}=\left(3;-7\right)\)
\(\left|\overrightarrow{a}\right|=\sqrt{2^2+5^2}=\sqrt{4+25}=\sqrt{29}\)
\(\left|\overrightarrow{b}\right|=\sqrt{3^2+\left(-7\right)^2}=\sqrt{49+9}=\sqrt{58}\)
\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\overrightarrow{a}\cdot\overrightarrow{b}}{\left|\overrightarrow{a}\right|\cdot\overrightarrow{b}}=\dfrac{-29}{\sqrt{29}\cdot\sqrt{58}}=\dfrac{-29}{29\cdot\sqrt{2}}=-\dfrac{1}{\sqrt{2}}\)
=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)=135^0\)
=>Chọn D
Câu 7:
\(\overrightarrow{a}=\left(2;1\right);\overrightarrow{b}=\left(3;-6\right)\)
\(\overrightarrow{a}\cdot\overrightarrow{b}=2\cdot3+1\cdot\left(-6\right)=6-6=0\)
=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)=90^0\)
=>Chọn B
Câu 8:
\(\overrightarrow{a}\perp\overrightarrow{b}\)
=>\(x\cdot2+2\cdot\left(-3\right)=0\)
=>2x-6=0
=>x=3
=>Chọn A
Câu 9:
\(\overrightarrow{u}\cdot\overrightarrow{v}=3\cdot\left(-8\right)+4\cdot6=-24+24=0\)
=>Chọn B
Câu 10:
\(C\in Oy\) nên C(0;y)
\(A\left(1;2\right);B\left(-3;1\right)\); C(0;y)
\(\overrightarrow{AB}=\left(-4;-1\right);\overrightarrow{AC}=\left(-1;y-2\right)\)
ΔABC vuông tại A
=>\(\overrightarrow{AB}\cdot\overrightarrow{AC}=0\)
=>\(\left(-1\right)\cdot\left(-4\right)+\left(-1\right)\cdot\left(y-2\right)=0\)
=>y-2-4=0
=>y=6
=>Chọn B
