Answer to Question #304985 in Mechanics | Relativity for Ogar Precious Owog

Question

a= 4i-2j-3k. b = 2i-j+6k. c=3i+j+k. Calculate 1). a+b+c. 2). a-b+2c. 3). do such that 2a-3b+D=0. 4). a.(b*c). 5). a*(bxc) 5). The angle between the vectors, a and b.

Answer 1

1)

$\qquad\qquad \begin{aligned} \small a+b+c&=\small (4+2+3)\hat i+(-2-1+1)\hat j+(-3+6+1)\hat k\\ &=\small 9\hat i-2\hat j+4\hat k \end{aligned}$

2)

• Add/subtract the coefficients of each unit vector just the same way done in the previous step.
• Additionally, vector c needs to be multiplied by 2 before adding.

3)

$\qquad\qquad \begin{aligned} \small 2(4i-2j-3k)-3(2i-j+6k)+D&=\small 0i+0j+0k\\ \small 2i-j-24k+D&=\small 0i+0j+0k\\ \small D&=\small -2\hat i+\hat j+24\hat k \end{aligned}$

4)

$\qquad\qquad \begin{aligned} \small b*c&=\small 11\\ \small a(b*c)&=\small 44i-22j-33k \end{aligned}$

5)

$\qquad\qquad \begin{aligned} \small b\times c&=\small -7i+16j+5k\\ \small a.(b\times c)&=\small -75 \end{aligned}$

6)

$\qquad\qquad \begin{aligned} \small a.b&=\small |a||b|sin\theta\\ \small \theta&=\small \sin^{-1}\Big[\frac{a.b}{|a||b|}\Big]\\ &=\small \sin^{-1}(\frac{-8}{34.5})\\ &=\small 166.6^0 \end{aligned}$