Related InterviewSolutions

• Show that the vectors ` vec a=1/7(2 hat i+3 hat j+6 hat k), vec b=1/7(3 hat i-6 hat j+2 hat k), vec c=1/7(6 hat i+2 hat j-3 hat k)`are mutually perpendicular unit vectors.
• Let ` vec a , vec b ,a n d vec c`are vectors such that `| vec a|=3,| vec b|=4a n d| vec c|=5,a n d( vec a+ vec b)`is perpendicular to ` vec c ,( vec b+ vec c)`is perpendicular to ` vec aa n d( vec c+ vec a)`is perpendicular to ` vec bdot`Then find the value of `| vec a+ vec b+ vec c|`.
• Find the angle between two vectors ` vec aa n d vec b`with magnitudes `sqrt(3)`and `2`respectively and such that ` vec adot vec b=sqrt(6.)`
• Dot products of a vector with vectors ` hat i- hat j+ hat k , 2 hat i+ hat j-3 hat k a n d hat i+ hat j+ hat k`are respectively 4, 0 and 2. Find the vector.
• Express the vector `vec(a)=(6hat(i)-3hat(j)-6hat(k))` as sum of two vectors such that one is parallel to the vector `vec(B)=(hat(i)+hat(j)+hat(k))` and the other is perpendicular to `vec(b)`.
• Let `vec(a)=(2hat(i)+3hat(j)+2 hat(k))` and `vec(b)=(hat(i)+2hat(j)+hat(k))`. Find the projection of (i) `vec(a)` on `vec(b)` and (ii) `vec(b)` on `vec(a)`.
• If ` vec a , vec b , vec c`are three vectors such that ` vec adot vec b= vec adot vec c`then show that ` vec a=0 or , vec b=c or vec a_|_( vec b- vec c)dot`
• If `vec a=3 hat i- hat j` and `vec b=2 hat i+hat j-3 hat k`, then express `vec b` in the from `vec b=vec b_1+vec b_2`, where `vec b_1|| vec a` and `vec b_2 _|_ vec a`.
• If ` vec a`and ` vec b`aretwo non-collinear unit vectors such that `| vec a+ vec b|=sqrt(3),`find `(2 vec a-5 vec b)dot(3 vec a+ vec b)`.