[" If "vec alpha=3hat imath+4hat j+5hat k" and "vec beta=2hat i+hat j-4hat k," then express "vec beta" in the form "vec beta=vec beta_(1)+vec beta_(2)," where "],[vec beta_(1)" is parallel to "vec alpha" and "vec beta_(2)" is perpendicular to "vec alpha" ."]

vec alpha=3hat i+4hat j+5hat k and vec beta=2hat i+hat j-4hat k then express vec beta in the form of vec beta=vec beta_(1)+vec beta_(2) where vec beta_(1) is parallel to vec alpha and vec beta_(2) is perpendicular to vec alpha .

If vec alpha = 3 hat i - hat j and vec beta = 2 hat i + hat j - 3 hat k , then express, vec beta in the form vec beta = vec beta_(1) + vec beta_(2) , where vec beta_(1) is parallel to vec alpha and vec beta_(2) is perpendicular to vec alpha .

If with reference to a right handed system of mutually perpendicular unit vectors hat i,hat j,hat k we have vec alpha=3hat i-hat j, and vec beta=2hat i+hat j-3hat k Express vec beta in the form vec beta=vec beta_(1)+vec beta_(2), where vec beta_(1) is parallel to vec alpha and vec beta_(2) is perpendicular to vec alpha .

If vec alpha=3hat i+4hat j+5hat k and vec beta=2hat i+hat j-4hat k then express vec beta in the form vec beta_(1)+vec beta_(2), where vec beta_(1) is parallel to vec alpha and vec beta is perpendicular to vec alpha.

If vec alpha=3vec i+4vec j+5vec k and vec beta=2vec i+vec j-4vec k ,then express vec beta in the form of vec beta=vec beta_(1)+vec beta_(2), where vec beta_(1) is parallel to vec alpha and vec beta_(2) is perpendicular to vec alpha .

If vec alpha=3 hat i-hat j and beta=2 hat i+hat j-3 hat k , express vec beta in the form vec beta=vec (beta)_1+ vec (beta)_2 where beta_1 is parallel to vec alpha and vec(beta)_2 is perpendicular to vec alpha .

If vec(a) = 3hat(i) - hat(j) and vec(b) = 2hat(i) + hat(j) - 3hat(k) then express vec(b) in the form of vec(b) = vec(b_(1)) + vec(b_(2)) where vec(b_(1))||vec(a) and vec(b_(2)) perpendicular to vec(a) .

If vec a=hat i+2hat j-3hat k and vec b=2hat i+4hat j+9hat k find a unit vector parallel to vec a+vec b

Let hat(alpha) = 3 hat(i)+hat(j) and hat(beta)= 2 hat(i)-hat(j)+3hat(k) . If vec(beta)=vec(beta)_(1)-vec(beta)_(2) , where vec(beta)_(1) is parallel to vec(alpha) and vec(beta)_(2) is perpendicular to vec(alpha) then vec(beta)_(1)xx vec(beta)_(2) is equal to :