`hat i.(2hat j times3hat k)+hat j.(2hat k times3hat i)+hat k.(2hat i times3hat j)` is equal to

Equation of the plane containing the lines vec r=(hat i-2hat j+hat k)+t(hat i+2hat j-hat k)vec r=(hat i+2hat j-hat k)+s(hat i+hat j+3hat k) is

Find the area of the parallelogram determined by the vectors: 2hat i and 3hat j2hat i+hat j+3hat k and hat i-hat j3hat i+hat j-2hat k and hat i-3hat j+4hat khat i-3hat j+hat k and hat i+hat j+hat k

[[[hat i+4hat j+6hat k,2hat i+ahat j+3hat k,hat i+2hat j-3hat k]=18 then value of a equals to:

Show that the points whose position vectors are as given below are collinear: 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-3hat k3hat i-2hat j+4hat k,hat i+hat j+hat k and -hat i+4hat j-2hat k

vec a=2hat i-hat j+hat k,vec b=hat i+2hat j-hat k,vec c=hat i+hat j-2hat k A vector coplanar coplanar with vec b and vec c whose projectin on vec a is magnitude sqrt((2)/(3)) is hat i+3hat j-3hat k b.-2hat i-hat j+5hat k c.2hat i+3hat j+3hat k d.2hat i+hat j+5hat k

A point on the line hat r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k be three vectors. A vector in the plane of vec ba n d vec c , whose projection on vec a is of magnitude sqrt(2//3) , is a. 2 hat i+3 hat j-3 hat k b. 2 hat i-3 hat j+3 hat k c. -2 hat i- hat j+5 hat k d. 2 hat i+ hat j+5 hat k

Prove that the following vectors are non- coplanar: 3hat i+hat j-hat k,2hat i-hat j+7hat k and 7hat i-hat j+23hat khat i+2hat j+3hat k,2hat i+hat j+3 and hat i+hat j+hat k

If t is a real number, and a vector vec r satisfies the equation vec r times(hat i-2hat j+hat k)=hat i-hat k , then vec r can be equal to- (A) hat j+t(hat i-2hat j+hat k) (B) hat i-hat j+hat k (C) 2hat i-3hat j+2hat k (D) hat i+hat k

Vectors perpendicular to hat i-hat j-hat k and in the plane of hat i+hat j+hat k and -hat i+hat j+vec k are hat i+hat k b.2hat i+hat j+hat hat k c.3hat i+2hat j+hat k d.-4hat i-2hat j-2hat k