Cross Product — Area, perpendicular vector

Q10.Let →a and →b be two unit vectors such that the angle between them is . If λ→a + 2→b and 3→a −λ→b are 3 perpendicular to each other, then the number of values of λ in [−1, 3] is : (1) 2 (2) 1 (3) 0 (4) 3 e 1 x x loge α

Q10.Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC , divides the arc −−−length of arc AB 1 → → → AC such that length of arc BC = 5 , and OC = αOA + βOB , then α + √2(√3 −1)β is equal to (1) 2√3 (2) 2 −√3 (3) 5√3 (4) 2 + √3 f ∘g is

Q23.Let →c be the projection vector of →b = λ^i + 4^k, λ > 0, on the vector →a = ^i + 2^j + 2^k. If |→a + →c| = 7, then the area of the parallelogram formed by the vectors →b and →c is ________

Q4. Let a line pass through two distinct points P(−2, −1, 3) and Q , and be parallel to the vector 3^i + 2^j + 2^k. If the distance of the point Q from the point R(1, 3, 3) is 5 , then the square of the area of △PQR is equal to : (1) 148 (2) 136 (3) 144 (4) 140

Q12.Let →a = 3^i −^j + 2^k, b =→a× (^i −2^k) and→c= b × ^k. Then the projection of→c−2^j on →a is : (1) 2√14 (2) √14 (3) 3√7 (4) 2√7

Q48.Two particles are located at equal distance from origin. The position vectors of those are represented by ¯A = 2^i + 3n^j + 2^k and ¯B = 2^i −2^j + 4p^k, respectively. If both the vectors are at right angle to each other, the value of n−1 is _____ .