सदिश `7bar(i)+bar(j)-4bar(k)` का सदिश `2bar(i)+6bar(j)+3bar(k)` पर प्रक्षेप लिखिए |

Compute 2 bar(j) xx (3bar(i) - 4bar(k)) + (bar(i)+2bar(j)) xx bar(k) .

If bar(a) = 2bar(i) + 3bar(j) + 4bar(k), bar(b) = bar(i) + bar(j) -bar(k), bar(c ) = bar(i) - bar(j) + bar(k) , compute bar(a)x(bar(b)xbar(c )) and verify that it is perpendicular to bar(a) .

Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k) .

bar (a) = 2bar (i) + 3bar (j) -bar (k), bar (b) = bar (i) + 2bar (j) -4bar (k), bar (c) = bar (i) + bar (j) + bar (k), bar (d) = bar (i) -bar (j) -bar (k) then

Prove that vectors bar(a) = 2bar(i) -bar(j) + bar(k), bar(b) = bar(i) -bar(3j)-5bar(k) and bar(c ) = 3bar(i) - 4bar(j) -4bar(k) are coplanar.

Let bar(a) = 2bar(i)-bar(j)+bar(k), bar(b) = 3bar(i) + 4bar(j) -bar(k) and if theta is the angle between bar(a), bar(b) then find sin theta .

If bar(a) = 2bar(i) +bar(j)-3bar(k), bar(b) = bar(i) -2bar(j)+bar(k), bar(C) =- bar(i) +bar(j)-4bar(k), bar(D) = bar(i) +bar(j)+bar(k) , then compute |(bar(a)xxbar(b))xx(bar(c)xxbar(d))| .