2nd PUC Mathematics Series 12

111. If AB × AC = 2i^−4j^+4k^, then the are of ΔABC is

112. |a × b|² + |a.b|² = 144 and |a| = 4, then |b| is equal to

113. If |a × b| = 4 and |a.b| = 2, then |a|² |b|² is equal to

114. The two vectors a = 2i^+j^+3k^ and b = 4 \hat{i}-\lambda \hat{j}+6 \hat{k} ae parallel, if λ is equal to

115. If |a|= 5, |b|= 13 and |a × b|= 25, find a.b

116. Find the value of λ so that the vectors 2i−4j^+k^ and 4i−8j^+λk^ are parallel.

117. The vectors AB = 3i^+4k^ and AC = AC=5i^−2j^+4k^ are the side of a ΔABC. The length of the median through A is

118. The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is

119. The vectors λi^+j^+2k^,i^+λj^−k^ and 2i^−j^+λk^ are coplanar if

120. If |a| = 4 and -3 ≤ λ ≤ 2, then the range of |λa| is