Projection of a vector

JEE Main Mathematics · Vectors · 13 questions, latest first

• Let a=2 i- j- k, b= i+3 j- k and c=2 i+ j+3 k. Let v be the vector in the plane of the vectors a and b, such that the length of…202624 January, Shift 2 · Q14
• Let a= i-2 j+3 k, b=2 i+ j- k, c=λ i+ j+ k and v= a × b. If v · c=11 and the length of the projection of b on c is p, then 9 p^2…202623 January, Shift 2 · Q15
• Let AB=2 i+4 j-5 k and AD= i+2 j+λ k, λ ∈ R. Let the projection of the vector v= i+ j+ k on the diagonal AC of the parallelogram…202622 January, Shift 1 · Q13
• Consider two vectors u=3 i- j and v=2 i+ j-λ k, λ>0. The angle between them is given by cos^-1((√5)/(2 √7)). Let v= v_1+ v_2,…20254 April, Shift 1 · Q16
• If a is a nonzero vector such that its projections on the vectors 2 i- j+2 k, i+2 j-2 k and k are equal, then a unit vector along…20252 April, Shift 1 · Q11
• If the components of a=α i+β j+γ k along and perpendicular to b=3 i+ j- k respectively, are 16/11(3 i+ j- k) and 1/11(-4 i-5 j-17…202528 January, Shift 2 · Q15
• 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:202524 January, Shift 2 · Q15
• 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…202522 January, Shift 1 · Q23
• Let O be the origin and the position vector of the point P be - i-2 j+3 k. If the position vectors of the points A, B and C are…202310 April, Shift 1 · Q16
• Let a=5 i- j-3 k and b= i+3 j+5 k be two vectors. Then which one of the following statements is TRUE?20231 February, Shift 2 · Q78
• Let a=4 i+3 j and b=3 i-4 j+5 k. If c is a vector such that c ·( a × b)+25=0, c ·( i+ j+ k)=4, and projection of c on a is 1,…202329 January, Shift 2 · Q76
• The vector a=- i+2 j+ k is rotated through a right angle, passing through the y -axis in its way and the resulting vector is b.…202325 January, Shift 1 · Q76
• Let α=4 i+3 j+5 k and β= i+2 j-4 k. Let β_1 be parallel to α and β_2 be perpendicular to α. If β= β_1+ β_2, then the value of 5…202324 January, Shift 2 · Q78