If `bar(a)=phat i+3hat j-7hat k,bar(b)=phat i-phat j+4hat k` and if the angle between `bar(a)` and `bar(b)` is acute,then the values of 'P' lies in

If vec(a) = hat(i) - 2 hat(j) + 3 hat(k) and vec(b) = 2 hat(i) - 3 hat(j) + 5 hat(k) , then angle between vec(a) and vec(b) is

If vec a=x hat i+(x-1) hat j+ hat k and vec b=(x+1) hat i+ hat j+a hat k make an acute angle AAx in R , then find the values of adot

If vec(A) = 5 hat(i) - 3 hat(j) + 4 hat(k) and vec(B) = hat(j) - hat(k) , find the sine of the angle between vec(a) and vec(B)

Let bar a= hat i+ hat j+ hat k ,""b= hat i- hat j+2 hat k and bar c=x hat i+(x-2) hat j- hat k . If the vector c lies in the plane of a and b , then x equals (1) 0 (2) 1 (3) -4 (4) -2

Write the value of [ hat i- hat j\ hat j- hat k\ hat k- hat i]

Show that the points A, B, C with position vectors 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the triangle.

Show that the points A, B and C with position vectors, veca=3 hat i-4 hat j-4 hat k , vecb=2 hat i- hat j+ hat k and vecc= hat i-3 hat j-5 hat k respectively form the vertices of a right angled triangle.

Write the value of [ hat i+ hat j\ hat j+ hat k\ hat k+ hat i]

If a=hat(i)+2hat(j)-2hat(k), b=2hat(i)-hat(j)+hat(k) and c=hat(i)+3hat(j)-hat(k) , then atimes(btimesc) is equal to

vec(A)=2hat(i)+4hat(j)+4hat(k) and vec(B)=4hat(i)+2hat(j)-4hat(k) are two vectors. Find the angles between them.