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If a=hat(i)+hat(j)+hat(k), b=hat(i)+3hat(j)+5hat(k) and c=7hat(i)+9hat(j)+11 hat(k), then the area of the parallelogram having diagonals a+b and b+c is |
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Answer» `4sqrt(6)` `a = hati +HATJ +hatk, b =hati +3hatj +5 hatj ` and`c=7 hati +9 hatj +1 hatk` Let `A =1 +b=(hati + hatj +hatk) +(hati+3hatj +5 hatk)=2 hati +4 hatj+6hatk` and `=+=(hat+hat3+ha5)+(hat7+hat9+hat11)` `=hat8+hat12+hat16` If A and B are adagonals, then area of parallelogram `1/2|AxxB|=1/2||{:(hati, hatj,hatk),(2,4,6),(8,12,16):}||` `=1/2|hati(64-72)-hatj(32-48)+hatk(24-32)|` `1/2|-8hati+16hatj-8hatk|` `=|-4hati+8hatj+4hatk|` `=sqrt((-4)^(2)+(8)^(2)+(-4)^(2))` `=sqrt(16+64+16)` `=sqrt96=4sqrt6` |
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