[" 21."5i+hat j-3hat k" wr "3hat i-4hat j+7hat k" का "" अदिग गुणनफत है "],[[" (A) "10," (B) "-10," (C) "15," (D) "-15]]

(4_(1)-25)r=[3hat i-7hat j+2hat k]=15,r=[4hat i+3hat j-5hat k]=16

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

If vec A=2hat i+hat j+hat k and vec B=7hat i+3hat j+hat k Find vec B timesvecA A) 19hat i-38hat j+16hat k B) 2hat i-5hat j+hat k C)- 14hat i+32hat j+hat k D) hat i+hat j+5hat k

Find the projection of vector hat i+3hat j+7hat k on the vector 7hat i-hat j+8hat k

Find the value of lamda , if the points with position vectors 3hat(i)- 2hat(j)- hat(k), 2hat(i) + 3hat(j)- 4hat(k), -hat(i) + hat(j) + 2hat(k), 4hat(i) + 5hat(j) + lamda hat(k) are coplanar.

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

Find ( vec (a) xxvec (b)) and |vec(a) xx vec (b)| ,when (i) vec(a) = hat(i)-hat(j)+ 2hat(k) and vec(b)= 2 hat(i)+3 hat(j)-4hat(k) (ii) vec(a)= 2hat (i)+hat(j)+ 3hat(k) and vec(b)= 3hat(i)+5 hat(j) - 2 hat(k) (iii) vec(a)=hat(i)- 7 hat(j)+ 7hat(k) and vec(b) = 3 hat(i)-2hat(j)+2 hat(k) (iv) vec(a)= 4hat(i)+ hat(j)- 2hat(k) and vec(b) = 3 hat(i)+hat(k) (v) vec(a) = 3 hat(i) + 4 hat(j) and vec(b) = hat(i)+hat(j)+hat(k)

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

Prove that the 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 are coplanar.