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Find a vector whose length is 7 and that is perpendicular to each of the vectorsvec(A) = 2 hat(i) - 3 hat(j) + 6 hat(k) and vec(B) = hat(i) + hat(j) - hat(k) |
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Answer» Solution :Given :`vec(A) = 2 HAT(i) - 3 hat(j) + 6 hat(K)` `vec(B) = hat(i) + hat(j) - hat(k)` Here ` vec(A) xx vec(B) |{:(hat(i),hat(j), hat(j)),(2, -3, 6),(1 , 1, -1):}|` `= hat(i) (3 - 6) - hat(j) (-2 - 6) + hat(k) (2 + 3)` `= - 3 hat(i) + 8 hat(j) + 5 hat(k)` `|A^(2) xx vec(B)| = sqrt((-3)^(2) + 8 ^(2) + 5^(2))` `= sqrt(98) = 7 sqrt(2)` Unit vector PERPENDICULAR to `vec(A) and vec(B)` is `hat(n) = (vec(A) xx vec(B))/(|vec(A) xx vec(B)|)= (-3 hat(i) + 8 hat(j) + 5 hat(k))/(7 sqrt(2))` Required vector `= 7 hat(n) = 7 ((-3hat(i) + 8 hat(j) + 5 hat(k))/(7 sqrt(2)))` `= (1)/(sqrt(2)) ( - 3 hat(i) + 8 hat(j) + 5 hat(k))` |
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