17th sum plz

Asked by lovemaan5500 | 7th Feb, 2020, 09:49: AM

Expert Answer:

Vertices B and C of triangle ABC lie along the line x+2/2 = y-1/1 = z-0/4
Vector along this line will be a with rightwards arrow on top equals 2 i plus j plus 4 k
Point lying on the above line will be (-2, 1, 0)
V e c t o r space j o i n i n g space t h e space p o i n t s space left parenthesis 1 comma space minus 1 comma space 2 right parenthesis space a n d space left parenthesis negative 2 comma space 1 comma space 0 right parenthesis space i s space 3 i minus 2 j plus 2 k equals b with rightwards arrow on top
N o w comma space A open parentheses triangle A B C close parentheses equals 1 half cross times open vertical bar A D close vertical bar cross times open vertical bar B C close vertical bar equals 1 half cross times open vertical bar b with rightwards arrow on top close vertical bar sin theta cross times open vertical bar stack B C with rightwards arrow on top close vertical bar
open vertical bar a with rightwards arrow on top cross times b with rightwards arrow on top close vertical bar equals open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar sin theta
rightwards double arrow open vertical bar b with rightwards arrow on top close vertical bar sin theta equals fraction numerator open vertical bar a with rightwards arrow on top cross times b with rightwards arrow on top close vertical bar over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction
B u t comma space a with rightwards arrow on top cross times b with rightwards arrow on top equals open vertical bar table row i j k row 2 1 4 row 3 cell negative 2 end cell 2 end table close vertical bar equals i open parentheses 2 plus 8 close parentheses minus j open parentheses 4 minus 12 close parentheses plus k open parentheses negative 4 minus 3 close parentheses equals 10 i plus 8 j minus 7 k
open vertical bar a with rightwards arrow on top cross times b with rightwards arrow on top close vertical bar equals square root of open parentheses 10 close parentheses squared plus open parentheses 8 close parentheses squared plus open parentheses negative 7 close parentheses squared end root equals square root of 100 plus 64 plus 49 end root equals square root of 213 space space a n d space open vertical bar a with rightwards arrow on top close vertical bar equals square root of 21
rightwards double arrow open vertical bar b with rightwards arrow on top close vertical bar sin theta equals fraction numerator square root of 213 over denominator square root of 21 end fraction
rightwards double arrow A open parentheses triangle A B C close parentheses equals 1 half cross times fraction numerator square root of 213 over denominator square root of 21 end fraction cross times 5 equals fraction numerator 5 square root of 213 over denominator 2 square root of 21 end fraction

Answered by Renu Varma | 7th Feb, 2020, 12:05: PM