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Syllabus

How to find whether the 2 line -6a+4b-8c& 2a+4b-2c are intersecting?

where a,b,c are vectors taken at random.

1. Find the sum of

$a)3{a}^{2}-6{a}^{2}-4{a}^{2},7{a}^{2}\phantom{\rule{0ex}{0ex}}b)7ab,8ab,-10ab,-5ab\phantom{\rule{0ex}{0ex}}c)6{x}^{2}y,-8{x}^{2}y,-4{x}^{2}y,3{x}^{2}y$

$\left(Answer:k=-\frac{8}{13}\right)$

$\frac{x-5}{3}=\frac{y-7}{-1}=\frac{z+2}{1}\mathrm{and}\frac{x+3}{-36}=\frac{y-3}{2}=\frac{z-6}{4}$ is

^{2 }+kxy + y^{2}= 0 is four times the other .1)2)Express the following in scientific notationa) 810000 b) 0.00081

3) Write the following in exponential form

a) Square of 3 b) Product of 2 cubed and 3 square

c) 5 raise to the power 7

a) Square of 3

b). Product of 2 cubed and 3 squared

c). 5 raise to the power 7

Please help in 4 th

Q. Convert into power notation

a. $\frac{-27}{125}$

b. $\frac{49}{81}$

$\mathit{Q}\mathbf{)}\mathbf{}\mathrm{Simplify}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{a})\frac{(24{)}^{2}\times {7}^{3}}{{8}^{2}\times 7}\mathrm{b})\frac{{5}^{3}\times {3}^{5}\times 6}{{3}^{2}\times 25}$