Introduction to Vectors

Given the vector  $<2,\ 2>,$  find the magnitude and direction angle it forms with the positive x-axis

•  $\left|a\right|=\sqrt{2}$  and  $\theta=\frac{\pi}{4}$  

•  $\left|a\right|=\sqrt{6}$  and  $\theta=\frac{\pi}{4}$  

•  $\left|a\right|=2\sqrt{2}$  and  $\theta=\frac{\pi}{4}$  

•  $\left|a\right|=2$  and  $\theta=\frac{\pi}{4}$  

Given the vector  $<\sqrt{3},1>,$  find the magnitude and direction angle it forms with the positive x-axis

•  $\left|a\right|=\sqrt{10}$  and  $\theta=\frac{\pi}{6}$  

•  $\left|a\right|=\sqrt{10}$  and  $\theta=\frac{\pi}{3}$  

•  $\left|a\right|=2$  and  $\theta=\frac{\pi}{6}$  

•  $\left|a\right|=2$  and  $\theta=\frac{\pi}{3}$  

Given the vector  $<-1,\ \sqrt{3}>,$  find the magnitude and direction angle it forms with the positive x-axis

•  $\left|a\right|=\sqrt{10}$  and  $\theta=\frac{5\pi}{6}$  

•  $\left|a\right|=\sqrt{10}$  and  $\theta=\frac{2\pi}{3}$  

•  $\left|a\right|=2$  and  $\theta=\frac{5\pi}{6}$  

•  $\left|a\right|=2$  and  $\theta=\frac{2\pi}{3}$  

Find the component form of the vector with magnitude of 4 that forms a  $\pi$  radians direction angle with the positive x-axis.

•  $<-1,\ 0>$  

•  $<-1,\ -4>$  

•  $<4,\ 0>$  

•  $<-4,\ 0>$  

Find the component form of the vector with magnitude of  $3\sqrt{2}$   that forms a  $\frac{\pi}{4}$  radians direction angle with the positive x-axis.

•  $<3,\ 3>$  

•  $<-3,\ -3>$  

•  $<3,\ -3>$  

•  $<-3,\ 3>$  

Find the component form of the vector with magnitude of  $10$   that forms a  $\frac{7\pi}{6}$  radians direction angle with the positive x-axis.

•  $<-\sqrt{3},\ -1>$  

•  $<-5\sqrt{3},\ -5>$  

•  $<-1,\ -\sqrt{3}>$  

•  $<-5,\ -5\sqrt{3}>$  

Let $u\ =\ <3,\ -2>$  and  $v\ =\ <-2,\ 5>.\ \$  Find the component form and magnitude of the vector  $3u.$  

•  $<9,\ -6>\ \ \ \left|a\right|=9\sqrt{13}$  

•  $<9,\ -6>\ \ \ \ \ \left|a\right|=3\sqrt{13}$  

•  $<-6,\ 15>\ \ \ \ \ \left|a\right|=3\sqrt{29}$  

•  $<-6,\ 9>\ \ \ \ \ \left|a\right|=\sqrt{117}$  

Let $u\ =\ <3,\ -2>$  and  $v\ =\ <-2,\ 5>.\ \$  Find the component form and magnitude of the vector  $u+v.$  

•  $<1,\ 3>\ \ \ \left|a\right|=2$  

•  $<5,\ -7>\ \ \ \ \ \left|a\right|=\sqrt{74}$  

•  $<1,\ 3>\ \ \ \ \ \left|a\right|=\sqrt{10}$  

•  $<-5,\ 7>\ \ \ \ \ \left|a\right|=\sqrt{74}$  

Let $u\ =\ <3,\ -2>$  and  $v\ =\ <-2,\ 5>.\ \$  Find the component form and magnitude of the vector  $2u-3v.$  

•  $<-13,\ 16>\ \ \ \left|a\right|=2$  

•  $<12,\ -19>\ \ \ \ \ \left|a\right|=\sqrt{505}$  

•  $<-16,\ 13>\ \ \ \ \ \left|a\right|=\sqrt{10}$  

•  $<12,\ -19>\ \ \ \ \ \left|a\right|=5\sqrt{101}$  

A particle travels in the plane with position vector  $r\left(t\right)=<3t^2,\ 2t^3>.$  Find the acceleration vector  $a\left(t\right).$  

•  $a\left(t\right)=<6,\ 6t>$  

•  $a\left(t\right)=<6t,\ 6t^2>$  

•  $a\left(t\right)=<6,\ 12t>$  

•  $a\left(t\right)=<6,\ 12>$